German right-wing party AfD has recently posted this claim on its Facebook page:

++ Neugeborene: Mohammed auf Platz 1 der Vornamen in Berlin ++

Man höre und staune: Der häufigste Erstname für neugeborene Jungen in
Berlin ist Mohammed. In Bremen liegt er auf Platz 3. Bundesweit ist
ein klarer Trend für die Top-10 der Namensregister absehbar.
[...]

Google Translation:

++ Newborns: Mohammed ranked first in Berlin ++

Just listen and wonder: The most common first name for newborn boys in
Berlin is Mohammed. He ranks third in Bremen. Nationwide, a clear
trend is foreseeable for the top 10 names.
[...]

This was also claimed by Daily Mail ("Mohammed was the most popular first name for boys born in Berlin in 2018, study reveals") and Breitbart ("Mohammed Number One Name for Baby Boys in Berlin").

German public radio then published a report on this claim (Google Translation) on their "Fact Finder" page, but I found that article rather confusing. I also tried to find one of the Fact Finder claims in the data published by the city of Berlin, but couldn't find it.

Can someone clarify whether the claim "Mohammed was the most popular first name for boys born in Berlin in 2018" is true?

No. Mohammed was not the most popular first name in Berlin 2018.

The official Berlin statistics conclude something different. And at the very least: It seems not likely to be possibly true, regardless of you twist the statistics. But it depends a bit on how you count names, and whether you do that in a consistent manner.

The official Ordnungsamt Berlin says the most popular first names were Emil and Alexander.
The next places were then occupied by Maximilian and Paul.

This is reported in accessible form on the TV news site rbb24:

Emil und Emilia waren 2018 berlinweit die beliebtesten ersten Vornamen für Neugeborene. In der Rangliste aller vergebener Vornamen konnten die Vorjahressieger ihre Spitzenplätze halten.
Ranking der ersten Vornamen
Das sind die beliebtesten Vornamen in den Berliner Bezirken
13.02.19 | 06:11 Uhr

To check for yourself official raw data from the Bureau of Statistics:

Berlin.de: Liste der häufigen Vornamen 2018, also on https://github.com/berlinonline/haeufige-vornamen-berlin

The most popular names as encoded for city quarters and as reported directly from the statistics bureau:

Treptow-Köpenick – Anton, Finn, Oskar

Tempelhof-Schöneberg – Noah, Paul, Jakob

Steglitz-Zehlendorf – Paul, Leonard, Leon

Spandau – Anton, Elias, Oskar

Reinickendorf – Amir, Elias, Liam

Pankow – Paul, Leon, Oskar

Neukölln – Ali, Adam, Noah

Mitte – Adam, Noah, David

Marzahn-Hellersdorf – Emil, Henry, Arthur

Lichtenberg – Emil, Leon, Anton

Friedrichshain-Kreuzberg – Emil, Alexander, Felix

Charlottenburg-Wilmersdorf – Anton, Emil, Maximilian

But there are slight problems with the statistic as read from the more easily found PDFs, which cut off the data after 'top 30 most popular names per district', which have quite a variance in population density and differing birth rates (but the full set of data is on github):

In Reinickendorf, where Amir was most popular, Mohamed/Mohamad comes in at 18/19 place (4 absolute for both, against Amir 6), making the name in question essentially top spot, if from the 30 presented names you normalise for spelling.

In Neukölln all name variants would place Mohammed at 2nd place, judged by the same limited PDF data.

Fact checking as done by TV news

As the ARD counted according to their understanding of the possible variants of for example Anton, Tony, Tonio etc we get a more impressive result for first names:

The name Mohammed appears 52 times as first name in the statistics, most frequently in the district Mitte: twelve times. If you now add different spellings of the name - for example Mohamad, Mohammad, Muhamnmed [sic!, LLC], Mohammed and others - you get about 280 first names - depending on which spellings you add.

But this also applies to other names: For example, the RBB counted variants such as Lukas, Lucas, Luka and Luca together - and comes up with far more than 400 hits, i.e. considerably more than for Mohammed.

Fact checking, and also source for some of the claims, from academic institution GfdS

The Gesellschaft für deutsche Sprache e.V. arrived at the following conclusion, nation-wide, out of 518.498 boys, spelling variants aggregated for all names (not just Mohammed, but even applying stricter rules for other names):

1. Paul


2. Alexander


3. Maximilian


4. Elias


5. Ben


6. Louis/Luis


7. Leon


8. Noah


9. Henry/Henri


10. Felix
    … …
    24 Mohammed

This nitpicking over spelling variants of essentially the same name seems irritating but the name Mohammed is a popular choice, originating from countries were the Arabic writing system usually leaves out the vowels. Add to that the dialects and the resulting variations in original Arabic spelling, the variety in transliteration to Latin script with vowels becomes apparent. Further, for a complete picture we have to add historic spellings from European languages, and Turkish.

The GfdS counts 25 variations of Mohammend and aggregates only 10 of those for their methodology. They say this is because in their eyes these would constitute "the same name, phonetically".

Short interlude:

What is the reason, for example for the Daily Mail, to assert that Mohammed would be the top spot?

The exact press release they claim to quote from the Deutsche Gesellschaft für Sprache says:

Auch Mohammed mit seinen zahlreichen Varianten steht in diesem Jahr in gleich drei Bundesländern in der Gesamtliste unter den Top 10: in Bremen, Berlin und im Saarland. Als Erstname ist er noch beliebter: In Berlin, Bremen, Hamburg, Hessen, Nordrhein-Westfalen und im Saarland ist er in der Erstnamenliste unter den Top 10 vertreten.
Mohammed with its numerous variants is also among the top 10 this year in three federal states: Bremen, Berlin and Saarland. As a first name it is even more popular: In Berlin, Bremen, Hamburg, Hesse, North Rhine-Westphalia and Saarland it is represented in the top 10 of the first name list.
_{(Src: Ausführliche Auswertung)}

Again: As a 1st 'first name', compared to 2nd 'first name' Mohammed is among the top ten in Berlin. It was not 'the first'. It only rises to the top in one of the sublists if you include variations of Mohammed quite generously but refuse to do so for other names.

Misreading, miscomprehending twisting facts

How anyone could jump from an already context-lacking and misleading "in the top ten in three cities" to even more distorting "most popular name in Berlin" seems a mystery. Unless you look at a table on the same page:

In that table you see:

Well. That table says that Mohammed was indeed the most popular name, over all. But only among Turkish/Arabic names isolated!

Using that table, the results published on that page is just not the correct way to interpret the data. A weakness of that table is further that they compare popular names in Turkey with 'Turkish/Arabic names in Germany'. By using the Arabic variant, not 'Mehmet', and not disclosing so far whether they do group both variants together in their counting method.

The problem: Not only spelling but also language and quite a bit of culture are quite different between 'Turks' and 'Arabs'. But the one thing in common: they are all perceived as 'Islam'. That looks like even in this institution the biases aren't balanced and controlled for.

The Breitbart headline is therefore just one word away from being true:

Mohammed Number One Name for Arabic Baby Boys in Berlin.

Although the corrected headline is not exactly 'man bites dog' quality.

The headline that German tabloid Bild makes of all this reads with a little more specificity:

Mohammed beliebtester Erstname in Berlin

That is: "Mohammed being the first first name is the most popular variation found in Berlin."

We already covered this above, but to be fair, at least that newspaper can claim to just quote the institution publishing their first name study:

(Src gfds: ausfuehrliche-auswertung-vornamen-2018)

Take note that this refers to 10 of 25 Mohammed variations grouped together while being less generous to other names. Also, the number in brackets indicates the real position in Berlin, again according to that way of counting. Naturally, the explanation and analysis is insufficient in the newspaper bit.

Analysis of raw data

However, my count arrives at 366 Mohammeds (normalised spellings & variants) as first first names and for Lukas its 432 first first names. So that's not true either

My own count through the source files gives for all first names (1st, 2nd etc) and all possible spelling variants (including Turkish and only part of a name) a count of 424 Mohammeds for male newborns in all of Berlin 2018.

This includes all variants I could find, including some appearing as 'more exotic', which would then include: Ahmed, Hemed, M'hamed, Mafumet, Magomed, Mahamed, Mahoma, Mahoma, Mahomet, Mahometus, Makhambet, Mamad, Mamadou, Mao, Maomé, Maomé, Maometto, Maxamed, Md, Mehmed, Mehmet, Mehmet, Mem, Memet, Mend, Mihemed, Mo, Moe, Mohamad, Mohamed, Mohamed, Mohammad, Mohammad, Mohammed, Mohammed, Mohd, Momo, Momo, Momodou, Muhamad, Muhamed, Muhameti, Muhammad, Muhammad, Muhammad, Muhammadu, Muhammed, Muhammed, Muhammed, Muhammet, Muhd, Moameth, Mahmet, Magomet, Mokhammed, Mukhammad, Mukhammed, Mukhammed, Mukhammad, Mat, Mokamat, Mù hǎn mò dé. ( = 62 variations.src1, src2)
But excluding derived names or merely related ones, like Ahmad, Hamid or Mahmud.

For comparison, the popular Alexander is almost as colourful:

Aale, Aca, Acika, Aco, Aki, Alakṣendra, Alasandar, Alasdair, Alastair, Alastar, Ale, Alec, Alecsandro, Aleixandre, Alejandro, Alejo, Aleka, Ālēkajānḍāra, Alekanekelo, Alekchendra, Alekos, Aleks, Aleksa, Sander, Aleksandr, Aleksandras, Aleksandre, Aleksandro, Aleksandrs, Aleksandŭr, Aleksanteri, Aleksas, Aleksi, Ales, Aleš, Alesander, Alesch, Alessandro, Alessio, Alex, Alexander, Alexandr, Alexandre, Alexandris, Alexandro, Alexandros, Alexandru, Alexei, Alexi, Alexis, Ali, Aliaksandr, Aliesch, Alisdair, Alistair, Alister, Aljaksandr, Alleksandeo, Alyeksandr, Alyel'ka, Arekisandā, Chandy, Eskandar, Eskender, Eskendir, Isikinidiri, Iskandar, İskender, Jandro, Léandre, Leandro, Lex, Lixandru, Oleg, Olek, Oleksandr, Oles', Olexander, Sale, Sander, Sandi, Sándor, Sandra, Sandre, Sandri, Sandro, Sandy, Sanja, Sanjetschka, Sanjka, Sanjok, Sanjuscha, Sanne, Santeri, Saša, Sascha, Sascha, Saschenka, Saschka, Saschok, Saschulja, Sashko, Sasho, Sašo, Schura, Schurik, Sekandar, Sender, Senderl, Sikandar, Skandar, Skander, Sonder, Tschander, Wander, Xande, Xander, Xandre, Xano, Xanocas, Xlĕksānde, Yàlìshāndà, Zander.

(src1, src2, 123 variations, all meaning 'Alexander'.)

As you can see from the huge list, these are not mere 'phonetic' equivalences or differences. Not all of these possible variations actually appear in Berlin. And in some cases it's far away from easy to decide whether Moe is named after a prophet or a barkeeper.

But for the actual name Mohammed it's noteworthy that it is a name that in studies that include ethnic status of parents is one that in stands contrast to eg Leila. One name has a high symbolic value, the other is often not even recognised as 'foreign origin'. Both names have a migrant background but almost only non-German parents might choose Mohammed, while Leyla gained some popularity in all groups. (Jürgen Gerhards: "Die Moderne und ihre Vornamen: Eine Einladung in die Kultursoziologie", VS Verlag für Sozialwissenschaften, Wiesbaden, ²2010, p134.)

As some of the more exotic variations for any name (eg Mo, Momo on the one side, Oleg, Lex for Alex) are ambiguous, we have to observe: There cannot be one exact and exactly correct solution for grouping the names by algorithm.

The methodolgy of counting at the GfdS

The Deutsche Welle reports and analyses:

The normally innocuous report, however, quickly became fodder for political mudslinging and false news reports — all because 280 of 22,000 newborn boys in Berlin were given one of at least 25 iterations of the first given name "Mohammed." […]

Lacking context
The GfdS report failed to provide much-needed context to its results, Gabriele Rodriguez, who researches family nomenclature at the University of Leipzig, told DW. This lack of clarity combined with a society sensitive to its changing demographics and mired in political debate over migration and refugee issues led to the groundswell of misinformation.
It's partly true that "Mohammed" has ascended the ranks of baby names due to growing immigrant communities in Germany. But it's also because it's tradition that families from the Arab world name at least one of their children after the Prophet Mohammed.

"There is not a large pool of names to choose from, as is the case with German families," she said, pointing out that over half of all baby names registered in any given year in Germany are unique, and that the most popular baby names are at most between 2% and 3% of all newborns.
And while most baby names have only a few different variations, there are at least 25 of the name "Mohammed." Moreover, it is often a first given name, causing it to occur with more frequency than other names in that category. The most popular name for boys in Berlin when all given names were taken into consideration was Alexander.
The GfdS study ranked Mohammed the 24th most popular name in Germany when second and third names were also taken into account.

Confusing methods

The report's methods were also not entirely fleshed out, said Rodriguez, making it difficult for the public to draw informed conclusions.
Until 2017's report, all first given names, regardless of order, were grouped together to determine the most popular. Over the past two years, however, the GfdS has begun to publish two separate lists together: The most popular overall baby names, including second and third given names, and the most common first given name on a birth certificate.
Without explaining the new methods for determining popularity, or giving absolute numbers for any given name, it's to be expected that the public would get confused, Rodriguez said.

"We also realized that the results are perhaps a bit confusing," Frauke Rüdebusch, a researcher with the GfdS, told DW. "But through the list of first given names, there is now another aspect of comparability that we didn't have before. Both lists are important for us … but [we] will be careful to ensure greater transparency and distinctness between the two."

Fearmongering

That the once innocent report got taken so out of context also speaks to Germans' fears of a changing society, said Rodriguez.
"Most new baby names in Germany are from abroad and are considered to be exotic — German ears need a bit of time to adjust," she said. "That's no problem in urban enclaves, but elsewhere people see that as a problem and feel threatened, even though in villages, where the problem is most pronounced, there are very few foreigners."
"This isn't just the case for first names — it has everything at the moment to do with foreigners," she added. "This is just feeding into the AfD, which has the express goal of creating fear about such things so that they can sustain themselves."

A poster for the AfD shows a famous painting of middle-eastern looking men checking the teeth of a woman (Getty Images/S. Gallup)
Researcher Rodriguez said the strong misinformed reaction to the name study had to do with German worries about migration, which the AfD is trying to capitalize on

DW: Berlin's 'Mohammed' baby-name trend distorted by far-right and media, Date 06.05.2019

As even the above analyses lacks some details about the methodology, let's look at that in as much detail as the GfdS allows:

Our method:

Homophonic names, i.e. names that are pronounced in the same way but written differently, are added together - in contrast to the lists sent to us by the individual registry offices. There is no difference here, the spelling is a matter of taste. So spellings like Sophie/Sophi/Sofie/Sofi or Louis/Luis etc. are treated like a name by us. A summary of names according to their etymology, i.e. their origin (e.g. Anna, Hanna, Jana, Johanna etc.) does not take place. Also names with different endings and/or different syllable numbers are not added together: Sophie and Sophia, Anna and Anne, Luca and Lucas are treated by us as two names each.

Variants of Mohammed:

With the name Mohammed we have summarized ten different writing variants, which are homophonic (identical sounding) or almost homophonic: Since this is an Arabic name and in Arabic the vowels are only inserted when speaking (depending on the speaker or dialect the name can assume a different pronunciation and thus a different transcription), we have not made any difference between variants with the similar vowels e and a (front/middle vowels) and o and u (rear vowels). The following spellings were summarized in our evaluation: Mohammed, Muhammed, Mohamed, Muhamed, Mohammad, Muhammad, Mohamet, Muhamet, Mohammet, Muhammet. Other possible spellings according to this scheme were very rare or did not occur at all. As independent names, we have treated etymological variants (i.e. names which originate from Mohammed, but which differ more in sound from the original name), such as Mehmet, Mahmoud, Mamadou, Ahmet, etc.

Variants of other names:

We have added together the most common phonological variants for the names mentioned. It cannot be excluded that other spellings also exist, but in a very small number.

Emil/Émile,
Anton,
Alexander/Aleksander/Alexandar/Aleksandar,
Karl/Carl,
Lukas/Lucas,
_{Src: direct communication, emphasis mine}

These decisions for counting are not the only ones possible. Some will say they may be 'reasonable', some will find them debatable, or wrong. They are not ideal, and no collection of decisions can be ideal.

Compare the following. For ideal German pronunciation: Mohammed [ˈmoːhamɛt], Muhammed [muˈhamð̩], or for ideal English pronunciation: Mohammed BrE /məˈhæmɪd/ ; NAmE /moʊˈhɑːmɪd/, Muhammad BrE /məˈhæmɪd/ ; NAmE /moʊˈhɑːmɪd/.

The following calculation is my own, and maybe faulty, but it groups names together based an linguistic heritage and shared meaning, so that for example most boys named after the prophet Mohammed, Mehmet, Magomet are in one group and Karl, Carl, Carlos, Charles are as well. Excluded are names that are derived and ambiguous. This is more inclusive than the GfdS method and naturally increases the numbers for all names across the board.

• For Mohammed and all its variants I arrive under the same criteria at 431.
  
  (54 when counting like a civil servant: only exact latinised spelling, only first first names, 2 compound names)




• For Paul and all its variants I arrive under the same criteria at 416.




• For Emil and all its variants I arrive under the same criteria at 497.




• For Friedrich and all its variants I arrive under the same criteria at 503.




• For Lukas and all its variants I arrive under the same criteria at 562.




• For Max and all its variants I arrive under the same criteria at 621.




• For Alexander and all its variants I arrive under the same criteria at 659!
  
  (174 when counting like a civil servant: only exact latinised spelling, only first first names, 7 compounded names)

There are still more Fritzen born in Berlin every year than Mohammeds!

That is for the etymological count of all first names, as seen above, including Friedrich and Fiete, and the same relational order again if you use exact spelling for first first name: Mohammed 52 versus Fritz 61.

For perspective, under again the same criteria including all first names this was out of 35148 names given for males (with ~40952 babies total).
Out of 22.157 newborn males in Berlin the GfdS counting used for all the headlines would give 257 Mohammeds as first first names in the variations included.

That makes for a share of 1.16% of all male newborns getting that name in some form. The current estimate of "somehow counted as Muslim" inhabitants of Berlin seems to be around 9%.
_{(Src for percentages: Mimikama: Der beliebteste Vorname 2018 ist… nicht Mohammed!)}

Sociological implications, or lack thereof

Since the headline making the claim in question is used for political purposes, matt_black in a comment below the question is right to note:

It is worth noting two observations from the UK data: 1) the Latin transliteration of the Arabic name is variable meaning that any single version of the Latin alphabet spelling will understate the popularity of the name; 2) the names of Muslim males lack diversity compared to other groups and this vastly overstates the relative popularity compared to the more diverse names typical of other groups.

It also doesn't mean that a name bearer has Muslim parents in every case. Berlin is an international city, but some 'very German' parents like colourful names and might name their children just after famous persons. Be them prophets or boxers seems of little importance in those cases.

The same argument is brought to German readers in
Martin Zips: "Warum der Name Mohammed so beliebt ist", Sueddeutsche Zeitung, 3. Mai 2019

And with another angle on "how-to-count first names" in:

"Mohammed in Berlin unter Top 10. Marie und Paul sind beliebteste Babynamen", Tagesspiegel, 02.05.2019

Since this is tagged 'sociology'

Bernd Matthie: "Populärste Vornamen 2018 – Kein Karl-Heinz", Tagesspiegel, 03.05.2019 and interestingly the same old tabloid Bild again: Knapp eins von 100 Babys heißt Mohammed Was sagt das wirklich über
Berlin aus?:

A closer look at the figures reveals that although Mohammed is the most common first name in Berlin, he is not necessarily a very common one. Of the 22,177 boys born in Berlin in 2018, 280 are called exactly like the Prophet of Islam. That is 1.26 percent of the male and 0.65 percent of all babies.

Please note that in their headline they equate "roughly 1 in 100 babies" with "0.65 of all males have some form of Mohammed in their given names list".

As one observable trend is that first names get ever more diverse and varied, especially in big cities like Berlin, a short look back for comparison:

In Regensburg in the 15th century, 22.6% of all male persons were already named Hans. In the 17th/18th century, when the custom of assigning several first names spread, Johann was almost regularly entered in the baptismal registers as the first first first name, followed by the actual call name in second place; just think of Johann Sebastian Bach, Johann Wolfgang Goethe and other famous namesakes.
_{Rosa Kohlheim & Volker Kohlheim: "Duden. Lexikon der Vornamen. Herkunft, Bedeutung und Gebrauch von über 8000 Vornamen", Bibliographisches Institut: Mannheim, 2007, p20. Take note that a previous edition listed 'only' 3000 first names for Germany.}

The biggest German TV station and its fact checkers, an academic institution, and yours truly, we all counted with a slightly different methodology. But the end result never changed.

The only angle to read the statistics that approaches "yep, claim checks out" is to count 'German names' nitpickingly strict like they appear in official statistics or just very slightly looser like the GfdS lists, but 'Arabic names' very loosely concerning the latinised spelling and aggregate.

In that case 'Mohammed' is in the top ten if you apply the aggregate counting method. The claim in question is only 'true' if using different methods of counting names on the same dataset for constructing this difference, and only for the popularity of that name in its assumed phonetic equivalence variants and as the first position of registering a name in a bureaucratic form – in absolutely no case for all first names – and thus false.

Looking at this from the other side: while not true in any meaningful way, even if we would accept the claim "most popular first first name in Berlin", then the conclusions drawn from this factoid by interested sides
would be less than impressive in absolute numbers. –– Unless of course, those opposing these private choices for naming babies, as they see it as a sign of 'islamisation', really desperately want to believe.

Conclusion

Expert opinions and my own analysis go all three in the same direction. No matter how you count first names, no matter how you spell and aggregate the variants, as long as you do that consistently for all possible first names in the same manner, then the result is always the same:

Mohammed was a somewhat popular name,

but Mohammed was not the most popular first name in Berlin in 2018 in any case.

The news origins from a statistic of the Gesellschaft für deutsche Sprache (GfdS). The Gfds made different Counts:

Mohammed is number one in Berlin, if you only take into account the first firstname. Example: If a child has the firstnames "Marie Paula", only Marie is counted not Paula.

If all firstnames are counted Number one for males in Berlin is Alexander, followed by Maximilian and Paul.

https://www.bz-berlin.de/berlin/mohammed-beliebtester-erstname-in-berlin

In Berlin war Mohammed im Jahr 2018 der beliebteste Erstname! [...] Wichtig: Die GfdS unterscheidet in ihrer Auswertung zwischen insgesamt beliebten Vornamen – dazu zählen ALLE Vornamen, neben Erstnamen also auch weitere Namen – und ausschließlich Erstnamen. Beispiel: Heißt ein Kind Marie Paula, ist Marie der Erstname, Paula der Zweitname. Beide Namen fließen in die GESAMTLISTE mit ein. In der LISTE DER ERSTNAMEN zählt jedoch nur Marie.

Translation:

In Berlin, Mohammed was the most popular first firstname in 2018! [...] Important: The GfdS distincts in its analysis between generally popular firstnames - counting ALL firstnames, besides the first firstname also additional names - and exclusively first firstnames. Example: Is a child Name Marie Paula, Marie is the first firstname and Paula the second firstname. Both names are included in the TOTAL LIST. However, in the LIST OF FIRST FIRSTNAMES only Marie counts.

https://www.deutschlandfunk.de/vornamen-ranking-marie-und-paul-sind-die-beliebteste.2849.de.html?drn:news_id=1002878

So I'm a new member without reputation.

But I did hear like what Leshie wrote in "Deutschlandfunk".
Don't know if that is available online. I did not find it.

So that, "Deutschlandfunk" is an official Radio Station usually receivable all over Germany, and
paid by https://www.rundfunkbeitrag.de/ which mainly everyone with a flat or an address in Germany has to pay.

Details regarding that in German language here:
https://www.rundfunkbeitrag.de/e175/e4794/Rundfunkbeitragsstaatsvertrag.pdf
.

They said something about first names of newborns in other big cities, which I unfortunately forgot.

It was a longer radio report (not so long, but longer than one sentence in the news).

They did a short interview with some people on the street. One said, he had like 12 Mohammeds in his family. And that
Mohammed is the best name. And that even Germans can name their children Mohammed.

edit:

so here is the link:

https://ondemand-mp3.dradio.de/file/dradio/2019/05/03/beliebtester_vorname_in_berlin_ist_mohammed_dlf_20190503_1426_c6e50d2c.mp3
but that is radio, only in german only sound.

They started, qouting this headline (refering to the printed paper):
https://www.bild.de/ratgeber/2019/ratgeber/neues-vornamen-ranking-2018-mohammed-beliebtester-erstname-in-berlin-61626786.bild.html

Later talking with this lady:
https://gfds.de/author/frauke/

here:
https://gfds.de/die-beliebtesten-vornamen-2018/
you may find something about Mohammed as a name.

And here:
https://gfds.de/wp-content/uploads/2019/05/Graphik-Bundesl%C3%A4nder-2018-neu-1.jpg
is the picture. Showing "Berlin - Erstnamen Jungen (first given names, boys) Mohammed." Bremen 2. and 3. - you may well read for yourself.

So, precisely for your Question, beside the text above your question, it's quite hard to give an answer.

I repeat your question:
one:

"Was Mohammed the most popular first name for boys born in Berlin in
2018?"

and the second question:

"Can someone clarify whether the claim "Mohammed was the most popular
first name for boys born in Berlin in 2018" is true?"

As the other answers already show, there are several problems to answer these questions.

Mohammed does not originate in the latin alphabet. Well other names as well.

Regarding the counting, the other answers give already a lot of information.

The Institute GfdS says so. They had this name in Berlin last year at place 6, this year at place one. Not counting all given names, but only the first of the given names of boys. As they published this two counts.

They counted Mohammed in his "numerous variants" and in this press release:
https://gfds.de/ausfuehrliche-auswertung-vornamen-2018/

they show a picture which shows, what I wrote above:
"They had this name in Berlin last year at place 6, this year at place one."

In the text in
https://gfds.de/die-beliebtesten-vornamen-2018/

they don't say that.

They write:

" Also Mohammed with its numerous variants is in this year even in 3
federal states in the total list under the top 10: in Bremen, Berlin,
and Saarland. As first given name it is even more popular: in Berlin,
Bremen, Hamburg, Hessen, Nordrhein-Westfalen and Saarland, is it in
the first given name list under the top 10."

I don't really understand the discussion.

It is not really new.

This is from 2003:
https://www.faz.net/aktuell/gesellschaft/europa-mohamed-ist-der-beliebteste-jungenname-in-bruessel-1143681.html
mohamed - in bruessel - belgium

This is from 2010
https://www.welt.de/vermischtes/article10580872/Mohammed-steigt-zum-beliebtesten-Jungennamen-auf.html

Mohammed in England and Wales
- "Mohammed in 12 variants, and so on the top"
This also from 2010
https://www.spiegel.de/panorama/gesellschaft/babynamen-englaender-nennen-ihre-jungs-am-liebsten-mohammed-a-725763.html

This from 2015:
http://www.kath.net/news/51688
again England and Wales, and variant of writing of the name

This is from 2018, Germany, Bremen:
https://correctiv.org/faktencheck/2018/05/11/ist-mohammed-der-beliebteste-vorname-in-bremen/

The GfdS counted with a sum of the writing variants, like the english shown above.

And the "municipal office of the interior" "Innenbehörde" of Bremen counted with the exact writing not summing up variants, having obviously a different count.

Rüdenbusch, is quoted with: "Sophie and Sofie is for us one name". A total of seven variants would be collected for the result.

They would be:"Mohammed, Mohamed, Muhammed, Muhamed, Mohammad, Mohamad and Muhammet"