The phrase, the United Kingdom should, in full, be the United Kingdom of Great Britain and Northern Ireland. Northern Ireland is now a province and Wales was a principality, so the only two kingdoms involved in the formation of the entity were those of Scotland and England.
If one of these erstwhile separate 'kingdoms' should leave the union, it's hard to see how the only remaining one can - even with Wales and Northern Ireland attached - still call itself the United Kingdom.
In addition, the earliest recorded use of the words 'Great Britain' was in 1604, at the time of the union of the crowns of Scotland and England. Again, therefore, it seems inappropriate that either phrase, "the United Kingdom" or "Great Britain" could be logically applied to a union without Scotland in it.
I am writing purely in terms of what words actually mean, as I do not think the inhabitants of Scotland will vote for independence next year. However, I really cannot see how current names can rationally just stay as they are if they do.