Correct and the breakup of the UK will likely lead to a United Ireland. The real question is what will England use for a TLD? They've never considered their place in the world that isn't in reference to the UK or GB because to them the two are interchangeable.
Things would need to be really, really bad for the Unionist population of NI before they'd vote to join Ireland. I'm honestly not sure that anything bar the total collapse of the other island would do it, tbh ;)
It's more the other way around. The Romans called the isles Britannia Major and Britannia Minor (now Great Britain and Ireland). Some time after Rome fell, Britons started to settle in another region they called Armorica, so it changed name to Brittany. "Small Britain" could be either Ireland or Brittany at this point.