A standard naming convention for specialized magic- (or magic-equivalent-) users; they are referred to as somethingmancers, and their specialized form of magic is called somethingmancy. The something is usually the Greek word for the thing or some other acceptably important-sounding term for it. As an example, death mages are known throughout all of fiction as necromancers. This structure makes it quite easy to create names for branches of magic using just about anything you can think of. You use fire? You're a pyromancer. Water? Hydromancer. Ice and cold? Cryomancer. It's that simple.