Not exactly, for two reasons. 
1: Physical geography entities (islands)
The largest of the British Isles is ‘Great Britain’. That’s independent of the country or countries occupying the landmass, which has existed since, ooh, the last Ice Age?
2: Sovereign entities (countries)
- Pre-1603: Scotland independent of England and Ireland.
England and Ireland in personal union (separate countries with the same monarch). - 1603: Scotland, England and Ireland all ruled by James VI and I, but formally three separate countries. No country of Great Britain yet!
- 1706-7 Acts of Union formally unite Scotland with England & Ireland, as two countries with one monarch: Great Britain and Ireland.
- 1800: Act of Union formally unites Great Britain with Ireland, as the United Kingdom of Great Britain and Ireland. ‘Great Britain’ the country formally ceases to exist.
- Irish independence: the Republic of Ireland revokes 1800 Act (as late as the 1960s?), which still applies in N.Ireland. I now agree that makes N.Ireland the rump of that kingdom. I have learned something!
So
- if Scotland leaves, no more country once-called ‘Great Britain’, but still occupying the island called Great Britain!
- If N.Ireland leaves and Scotland stays, I suppose ‘Great Britain’ could exist again, though ‘United Kingdom (of England and Scotland)’ seems more likely.
- If both leave, no more UK at all.
- If Wales leaves… well, we weren’t counted in the name(s) anyway…
Can’t we all just stay in the EU? It’s simpler.
