She was born Elizabeth Alexandra Mary - HRH Princess Elizabeth of York - daughter of the then Duke and Duchess of York and granddaughter of HM King George V and HM Queen Mary. Before she succeeded to the throne on the death of her Father, HM King George VI, in 1952, she had not been Princess of Wales in her own right as heir. She was simply HRH The Princess Elizabeth as only the eldest surviving son of a Sovereign can take on those titles. When she married Lt Sir Philip Mountbatten who had just been created Duke of Edinburgh in 1947 she again simply became HRH The Princess Elizabeth, Duchess of Edinburgh.
Before she became monarch, Princess Elizabeth could not assume the plain white Label of an heir apparent because, under male-preference primogeniture, she was heiress presumptive. The difference then was that a younger son could take preference over an elder daughter. Princess Elizabeth had a younger sister, Princess Margaret Rose, but was heir to her Father only under the "presumption" that a third child to her parents wasn't a boy. Practically speaking this "presumption" became less and less likely over the years and so Princess Elizabeth could be trained to take over the reins.
Instead of the plain white Label, Princess Elizabeth was treated like a Princess Royal and was assigned a three-pointed Label with a central Tudor Rose and two St George's Crosses. This was done in 1944 when Princess Elizabeth became 18, though at the same time, her sister, Princess Margaret Rose, was assigned her Label almost so that she wouldn't feel left out at the age of 14.
Many Happy Returns, Your Majesty!