According to Churchill's history, the word Britain derives from Pretani, a pre-Roman tribe. The term, British Empire, shows that the constituent nations have not always squabbled among themselves for pride of position. Or maybe it was because it singled none of them out for particular blame. Today, the term British Isles is mainly used by television weather forecasters. This enables them to put rain cloud symbols over the whole of Ireland without causing political offence. The Irish, I believe, do not have a special word the other islands in the group. I think this is because they had already colonised all of them before British history proper began - with, of course, the normans.