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I think 'stocker' is a common term for this in the US, though it may have declined with the rise of more business speak terms.

In the UK I have heard and seen shelf-stacker or sometimes shelf filler to describe this role.

Someone whose job is to put goods on the shelves in a supermarket - Cambridge Dictionary

A person whose job is to fill the shelves and displays in a supermarket or other shop with goods for sale - Collins Dictionary

A person whose job is to fill the shelves and displays in a supermarket or other shop with goods for sale - Dictionary.com

Similar definitions are also in The Free Dictionary

Some companies or staff (rightly or wrongly) may want to overstate a job title, a job advertised as a merchandiser or product placement specialist (another actual, but different job role) may attract more applicants than advertising for a shelf-stacker; also an employee needing to ‘enhance’ their cv.

So you are correct that merchandiser is the wrong term.

In my state (MA) in the US, they call it a "stock boy".

In a lot of companies in the US, this job is called "stock associate."

The responsibilities can include receiving shipments, stocking items in warehouses or on sales-floors, and assisting customers.

Other possible terms are "store clerk" and "salesclerk."

Stock clerk is a term I have often heard and seen. It's widely used in job descriptions and job search sites, though Stock Associate has become more popular in recent years.

shelf-stacker would be term used in the UK, Australia and New Zealand. A merchandiser works for the manufacturer or supplier of a product and visits stores to set up the shelves and/or in-store displays.

To add on to the other answers (stock clerk, stocker, stock associate, store clerk, sales clerk, etc.):

In some libraries, this job is literally called a shelver (although "re-shelver" might be more accurate).

The general terms given here are all applicable. You asked specifically about grocery stores and when I was in the grocery business we called them "grocery clerks." We called the group who did this work the "grocery crew" or "grocery" for short. This was to distinguish them from the produce, bakery, meat and front-end (cashiers and administrative workers) crews.

Grocery crews had responsibility for making sure the non-perishable goods were well stocked and properly rotated (newer products went to the back of the shelf and worked their way forward). The perishable products were handled by crews that specialized in that particular product which sometimes had a specialized skill; meat cutter for the meat department or baker for the bakery, as examples.

Different geographic areas and different companies had some slight variations in the naming of the position and some of those variations included the more generic title seen in other answers, such as stocker.

I used to do this as a job in Australia, our official title was 'Fill Associate' (as we filled the shelves) and we were more colloquially referred to as 'Fillers' or just 'Fill'

I would say stock boy or stock person. (There seems to be regional variation in this, I am in the North-east U.S. if that helps.)

In french we use the word "magasinier", which can be translated to "storekeeper" or "warehouseman".

I think a storekeeper has a interactions with the customer (such as advising) and manages other aspects of the shop such as the cash register. He actually keeps the shop, so it may not be what you are looking for.

In the other hand, warehouseman induces the idea of a large scale of merchandise, so your choice depends on the context.

I've been called a "Merchandiser" by the large box store where I used to work.

Other people have left reviews for this position

I don't know about the UK, but in America we call them
Stocker/Sales Associate: person who "stocks shelves
Vendor: someone from outside of the store who sells the products and maintains the needs of the product/company.