Assuming, for the sake of argument, that Scotland chooses her own path and makes her own way in the future (an episode of Doctor Who presaged this not too long ago), what should the remainder of the United Kingdom – currently denominated, "of Great Britain and Northern Ireland" – be called? Before Eire won her freedom, it was the United Kingdom of Great Britain and Ireland; and before Ireland was incorporated fully, it was the Kingdom of Great Britain, once the old Parliament of Scotland had voted for union, and her own dissolution, back in 1707.
How about the United Kingdom of England, Wales, (Cornwall*) and Northern Ireland? Or, perhaps, the United Kingdom of 2/3 of Britain and 1/6 of Ireland?
In any case, Her Majesty would still rule over both this successor state, and the restored Kingdom of Scotland; this would be but the latest division of the Crown, just as she rules as Queen of (the Dominion of) Canada, of the Commonwealth of Australia, and so forth.
* Some assert that Cornwall was never fully incorporated into England.