There are so many, I wouldn’t even guess at the total number. As you have already discovered, many are named after a small, or large specific region or city, so the list goes on and on, but in general terms, we typically refer to pizzas as follows:
New York Style
Chicago Deep-Dish
Chicago Stuffed
Chicago Cracker
St Louis Thin Crust
Brick Oven
California Deep Dish
Neopolitain
Sicilian
Tom Lehmann/The Dough Doctor