For example, a demonym is the name given to the inhabitants of a particular location.
Demonym: United States -> American
Is there a word for the name given to people that do a certain job?
(Word I'm looking for): Cooking -> Cook
Closest thing I can think of is job title, according to Collins Dictionary:
a name that describes a person's job in an organization
And their example sentence:
My official job title is Deputy Manager.
Cook is probably not a full job title, most kitchens have more than one cook and they have different titles (somewhat similar to military ranks, but even more specific to what they actually do, rather than just indicating a hierarchy). Wikipedia has quite an extensive list, including but not limited to the following job titles (French in brackets, although the French title may be used in England as well):
head chef (chef de cuisine)
deputy chef (sous-chef; this probably more common than the English version)
pastry cook (pâtissier)
1 "Job Title Definition and Meaning | Collins English Dictionary." Complacent Definition and Meaning | Collins English Dictionary. Accessed May 05, 2018. https://www.collinsdictionary.com/dictionary/english/job-title.