I'm Irish and I've always found the controversy a bit ridiculous; it's a classic example of Irish people's distaste for all things English being taken to a nonsensical extreme. You never hear Brits complaining about the Irish Sea being called such.
I don't know, given the Isle of Man is in the middle of it, maybe it should be The Manx Sea? If we don't want anyone to own it, maybe call it The Sea of Sodor?