What do you call a person who works at a supermarket?

There are tons of positions within a grocery retail company.

As far as at a specific retail location or store, there are:

Managers:

Store Manager

Assistant Manager

Grocery Manager

Customer Service Sales Manager

Assistant Customer Service Sales Manager

Manager of Produce

Meat Market Manager

Deli/Baker Manager

Frozen Food and Dairy Manager

Associates:

Sales Associates (Cashiers)

Service Associates (Baggers)

Grocery Associate (Stockers)

Office assistant

Scan Analyst

DSD Receivers

HBC Department

Produce Department

Meat Department

Deli/Bakery

FFD Department

Pet care departments

Wine and Beer Departments

Pharmacy

Security

That is in the store alone. However there are tons of other positions available in a grocery company that are not in one specific store (ie. Warehouse workers, truck drivers, district managers, CEO, president, marketing directors)