For the vast majority of people here the collective term for the British Isles is the British Isles and of course in truth it always has been. There are now some Irish who dislike this term and look for alternatives. I 'suppose' they dislike the term for political reasons and because they think it implies that the islands belong to Britain but of course that is not so. The term Pretanic or Britannic isles etc was coined in "whenever BC" millenia before the formation of Great Britain and before the largest island itself was even called Britain. So in realty it is akin to some Canadians suddenly disliking the term North American Continent because the term America is already part of their neighbour's name.