Great Britain and Ireland
Ok, here's a question what is "Britain"? Before independence Ireland was part of "The United Kingdom of Great Britain and Ireland". After the Republic became independent the name changed to Great Britain and Northern Ireland. Great Britain was the combined kingdoms of England and Scotland so wouldn't that, to some degree, indicate Britain is the island as a whole (does Wales fall under the Kingdom of England???). Add to that the face that the island was called Britannia by the Romans while Ireland was called Hibernia. So prior to independence wouldn't an Irish person still have been Irish not British.