In any event, this was all resolved in 1953. John MacCormick and Ian Hamilton contested the right of the Queen to call herself "Elizabeth II" in Scotland. They claimed it was a breach of the Treaty of Union 1707 between England and Scotland, since Elizabeth I had been Queen of England but not of Scotland.
The court noted that MacCormick and Hamilton had not brought the claim out of criticism of the Queen or disloyalty, but merely regarding symbolism. The court ruled that there had been no breach of the Treaty of Union, they had no jurisdiction to interfere and essentially the Queen could use whatever title she wished. This was then confirmed upon the creation of the Scottish Parliament in 1999.