It can't be Gavin Newsom for the same reason Trump couldn't have Rubio - you can't have two people from the same state on the ticket. I'm not sure what would happen if Beshear did resign to become VP as far as who becomes Kentucky's next governor.
Another name I've heard as a VP candidate is Roy Cooper - he's the outgoing governor of North Carolina who's term limited and wouldn't be running for any other office right now.