Yes, Parmigiano Reggiano is named after the provinces of Parma and Reggio Emilia, where it was originally produced. Now Parmigiano Reggiano is a Protected Designation of Origin and can be produced in a small amount of italian provinces, including Parma, Reggio Emilia, Bologna and Modena. Emilia Romagna is a wonderful place and probably is one of the italian Regions where you can eat better, is has so many food specialities and different plates!

In my head they all have a wooden leg like pirates.

I know you are making a joke and I laughed, but fun fact: Prosciutto crudo di Parma DOP (PDO) is a Protected Designation of Origin, so if it's made outside of Parma it's "just" Prosciutto crudo. Another fun fact: I am not fun at parties!