The name of fitness instructor is actually normal, because what's his name? It will bring you closer, and the coach is actually your teacher, so if he calls you a classmate, it is actually a way to pull you between you two. Think about it. I want to see if it's strange if he calls you by your first name or directly by your first and last names. And fitness itself is a very relaxing exercise, so there is no need to be so formal.