The thing with influence is that it's only one level down. You get 1 point for the vassal and 1 more for each one of his territories. But you get nothing for his own vassals. Basically, it's theoretically possible for a vassal to become stronger than his liege. That free territory is weird... But as...
I agree absolutely. There should be a way to rename a dynasty. For now I just renamed it for you. However, the new name is not going to appear before your next game.