Interesting take. Try telling Nadine Coyle she has a British accent?

Given that the people of Ireland reject that name, it's a very British thing to deadname them.

Serious answer - no Prythonic speakers lived in Ireland, so there is no proper basis for the name beyond people quoting a Greek who had never been there. It fell out of use for a millennium and was revised by a Welshman who spoke to angels as a way to erase the separate identities of Scotland, Wales and Ireland. His reasoning was that the King of the Britons, Arthur, had conquered Ireland (if he ever existed, he did not). I am speaking of John Dee who also coined the terms British Empire (it stuck) and British Ocean (it decidedly did not).

Why can't England be part of the Irish Isles?