Re: What's in a name?
They could just change the name from The United Kingdom of Great Britain and Northern Ireland (yes, that's the official name, look at your passport) to The United Kingdom of England, Wales, and Northern Ireland.
Although now that I think about it Great Britain is a geographical entity (it's the island upon which we live), not a political one, so they could actually keep the name as the country will occupy the bulk of the island.