Dynasty

A dynasty is a sequence of rulers from the same family, whether it be by blood or by honorary status.

Tales
The Isle of Pony may have been a dynasty, as it was ruled by a king, Queen and a Rosey

Friendship is Magic
While Equestria is not exactly a dynasty in of itself, the Crystal Empire appears to have been one, as Princess Cadance and Radiant Hope both appeared to be members of the Amore bloodline.