Great Britain is a geographical term, not a political one.
It refers to the biggest island in the two island British Isles (the other island being Ireland).
If Great Britain is no longer United, then the name cannot stand.
England is a country, Wales was annexed and was a principality but the Welsh Assembly now designate it as a country. Northern Ireland is a province.
We could probably get away with the United Kingdoms of England, Wales and Northern Ireland (UK for short).