Yes, what I mean is simply this. The UK is a Union of Great Britain and Northern Ireland. GB is a Union of England (then included Wales) and Scotland. If Scotland departed, GB would be annihilated in anything resembling its present form; and in that case the United Kingdom of Great Britain and Northern Ireland would also be disrupted because one of its components (GB) had undergone dissolution or at the very least, gross mutation.
If, thereafter, the governments of England, Wales and N Ireland desired to form a new union, they could call it "The United Kingdom", or anything else that might take their fancy, but the original UK would be no more.