The name (at present) is the United Kingdom of Great Britain and Northern Ireland. Again, UK is just a handy abbreviation and would presumably continue to be used, albeit with a different meaning, if the Scots vote to leave.
Great Britain means England Wales and Scotland. The term Britain used to be applied to mean Wales, and subsequently it meant England and Wales. It has fallen out of use as such, but could be resurrected as the United Kingdom of Britain and Northern Ireland.....