Éire is just the Irish word for Ireland, as in the whole island of Ireland. It’s not flavour of the month because it’s use inherently claims jurisdiction for the Republic of Ireland over the whole island. It does get used by hardliners, and was used more prior to Ireland joining the EU. ‘Southern Ireland’ is a term used by simpletons who’ve never bothered to look at a map - the most northerly points of the island are in the Republic, that’s why ‘Northern Ireland’ isnt ideal either. When the U.K. divided the island they made sure to keep as much of the then prosperous north east as possible, and at partition the counties that remained in the U.K. were responsible for 80% of GDP - of course, those counties are now totally dependent on state aid and the nationalists there are quiet happy to keep it that way - the bigger drain the better. The DUP and fellow travellers sometimes refer to the six counties in the U.K. as ‘Ulster’, as if the arbitrary border had some justification in ancient history, but three of the counties of Ulster are actually in the Republic. Really, the only accurate name for the six counties in the U.K. is ‘The Six Counties’, because there was no justification for creating the six county state, except that many of the population in those counties are descended from British settlers who arrived four hundred years ago. The demographics now are quite interesting. Only two of the six counties now have clear unionist majorities. The unionists want to stay in the U.K. for as long as possible to put as much time between the days when they treated the nationalists as second class citizens and eventual unification as possible. The nationalists are pretty close to being in the majority now, but they won’t vote for unification whilst they can still manage to make partition profitable for themselves and painful for Britain. When they do vote for unification, if the unionists behave as they did in the past, and if the British government support them as they did in the past, then they will demand a new partition, with this time, just Antrim and Down in their statelet. Not sure it would work though, especially as most of Belfast tends to vote Sinn Féin.