Bomber jackets with patches, aviators, flight suits, toy jets—Top Gun has all of these things and more.
Like the dog tags, all this other stuff is meant to evoke Navy culture—to give the viewer a sense of what the world of the naval aviators is like. Everybody in the film can be seen with some or all of this different swag at one point or another: Maverick has his jacket, as does Charlie. Sunglasses are everywhere. Slider is playing with a toy jet in the scene where Charlie invites Maverick over for dinner. The room in which the first Top Gun lesson takes place is full of toy jets, patches, and the like.
The Top Gun pilots are naval aviators, and they're proud of it. It's almost like they're a part of a major college football team or something like that, and feel the need to represent their "school" (the United States Navy) every chance they get. This is exactly what the writers wanted. They wanted Top Gun to be, essentially, a sports movie, with aerial combat the sport.