I don't think this historical matter is going to be relevant. The leftover bits will want to claim continuity with the preceding state, and they will want to use the UK name. But even if there's no consideration giving to branding, thanks to the Welsh Senedd there's now a distinct category of Welsh law, different from English law. So while the union of England and Wales might have been brought about by the extinguishment of the Welsh state, such as it may be, the union is being continued through the regeneration of some of the aspects of statehood.
