Board Thread:General Discussion/@comment-32710756-20170803144728/@comment-28895263-20170804034541

Without a direct heir, the powers-that-be would search the family tree for more distant living kin: cousins, or nephews. This is covered in the books, somewhat: there's a scene where Littlefinger is telling Sansa who becomes Lord of the Vale if young Robert (Robin) Arryn dies childless.

Such an heir might not have the family name. I suppose that can be fixed by royal decree.

Or... "spoils of war". Highgarden could be turned over to another lord, as Sansa wanted to do with Karhold and The Last Hearth.