[quote=The Nexerus]
The Republic of Ireland didn't make its name "The Republic of most of Ireland" just because Northern Ireland chose to stay in the U.K. The U.K. would, obviously, keep its name exactly as it is: the United Kingdom of Great Britain and Northern Ireland. The fact that it would not constitute the whole of Great Britain any more wouldn't warrant a name change.
[/quote]

I shouldn't have to specify, but I was making a joke.