I think custom tags should form when countries of similar size (or with a similar number of cores) fusion. The Commonwealth (of Poland-Lithuania) is a perfect example here, as is the United Kingdom (even if Scotland is smaller than England).
I wouldn't mind if the player could rename at will every country name in the game. However, I wouldn't like, as others said, if the AI renamed itself for no good reason. A dramatic change of primary culture (as if an Austria reduced to Hungary would have renamed itself Hungary) or an integration after a personnal union between two countries of a similar size (England-Scotland, Castille-Aragon, Portugal-Castille) comes to mind. Keeping the same name would then have been a slight for the country, enough to destabilize the new union. So it was necessary to rename the whole.