That's not a chef. Hell, at best you're describing the sous chef. Even then, its usually just staff.

A chef usually goes to a professional school. Typically in France. And when they get their restaurant, their duties are far more creative. They are sourcing foods, building a menu, etc. Then they pretty much make everyone staffed in the kitchen is carrying things out to a T.

Tyler could become a chef. Even without the schooling. But it won't be because he just dropped some stuffed mushrooms in the friar. Chefs are picked by restaurant investors that are staking a lot of money on a property and usually have to be able to parade their chef in advertising to get people in the door. A chef either needs credentials (fancy French school) or a reputation from working at some other wildly successful place.

But no, it's not just 'head cook'.