Great question on the beeb site.
Personally I don't think it will happen, but hypothetically if it did, would we have to rename the UK?
"The rest of the UK" is the handle used most commonly - it appears 293 times in the Scottish Government's white paper on independence - but leaves England, Wales and Northern Ireland in danger of sounding like Scotland's cast-offs. It's also a bit of a mouthful.
Its abbreviation, rUK, is already used by Scottish universities to differentiate between students from Scotland and those from the rest of the UK in relation to tuition fees. It regularly appears in Scottish newspapers such as the Herald and Scotsman."
www.bbc.co.uk/news/blogs-magazine-monitor-27867406
Maybe them and us? Like the suggestion of Former UK and it's abbreviated initials 
, French might get a bit upset 
