Perrin/Faile will rule the Two Rivers and Faile/Perrin will rule Salaea, but it won't be new joint nation.    Perrin has sworn fealty to Andor for the Two Rivers, but it's largely autonomous.  Perrin will do what he can to protect that autonomy, but he won't break with Andor unless Elayne forces that extreme action on him.    I don't see Perrin doing any sort of direct rule over Ghealdan, although some degree of influence and interaction is likely.

It would make sense to appoint Tam, the father of the Dragon Reborn.  After all Perrin has no children yet so who better to be the steward of the Two Rivers.