A mattress maker is called what? I'm looking for an older description, the oldest the better. Is there a name for this profession?
No special word. "Mattress maker" or "Mattress manufacturer" would be most easily understood.
Modern mattresses are made in factories by industrial processes. In the past and in craft contexts, adding cloth and cushioning to furniture is called upholstery, and is the job of the upholsterer, but they would be more concerned with adding cushions to seats than with making mattresses.
In the mediæval period, a mattress for all but the very richest would be a hemp sack (called a tick, but that meaning is not obselete), stuffed with straw, not requiring a skilled manufacture. - source