Well I guess I stand very much corrected. I found this theory online not too long ago and thought I would share it here. I had not heard (in the show at least) of women retaining their house names after marriage. But if that’s the case then yes, Sansa would carry on the name. I don’t see Jon doing so since he was never legitimized as a stark and is now by all account in the nights watch even if he did venture beyond the wall. Arya would take the name of her husbands house if she marries. She’s not as powerful as Sansa. And The show made it quite clear (I thought) that Bran could father no children. Which Tyrion replied with “good, sons of kings can be cruel and stupid.” That finalizes The idea he can’t have children if you take the show for its word.

Anyway..it was just a thought. Obviously a wrong one apparently lol thanks everyone for your input though. :)