Formal:
* Dishwashing specialist
* Dishwashing technician
* Dishwasher (can refer to the machine or the person)
Informal:
* Dish washer
* Scrubber
* Washer
* Cleaner
* Pot scrubber (if they also wash pots and pans)
* Sudie (slang term)
The best word to use will depend on the context. If you're writing a job description, you might use a more formal term like "dishwashing technician." If you're talking to a friend, you might use a more casual term like "dishwasher" or "scrubber."