Yes, we need Name+Surname, so the problem will be solved.
See this could work, but only up to a point. My mains name is just Ungermax, no surname. Someone else has it on Orien. I would have moved long ago if it wasnt for that. I know plenty of people on Thelanis that dont have surnames.
For transferring to non-Cormyr 64 bitters, they could just add a 3rd name field that is automatically filled for you ie "of Thelanis." Have this mandatory 3rd name visible only when someone examines your character or sees you in the social panel. Maybe with a toggle option to display it normally.