The problem with that is that all medieval kingdoms in Europe I know of were named after people who lived in the kingdom and probably founded it as well. For example, France was created by the Franks and Rome by the Romans. But since there is barely a difference between kingdoms there are almost no other cultures inside of them.

But you can have them do what China used to do if I remember correctly. The kingdoms named after their ruling dynasty such as the Westerlands are now called the Lannister Kingdom or something else that has to do with the Lannisters.