Marc is absolutely correct, this has been the practice for British royals for generations.
Wives of British princes automatically take the female equivalent of their husband's title BUT they are not accorded the title of 'Princess' before their given names UNLESS they are Princesses by birth themselves. eg, when Lady Diana Spencer married Prince Charles, Prince of Wales, she became Princess Charles, Princess of Wales, the same as when Baroness Marie Christine von Reibnitz became Princess Michael of Kent when she married Prince Michael of Kent. Diana was NEVER Princess Diana, Princess of Wales but after her divorce with Charles, she had all the rights to address herself as The Lady Diana, Princess of Wales, with the title of "Lady" owed to her birthright as a daughter of an Earl. However, princesses by birth who married into the family are allowed to use such title as in the case of Princess Marina, Duchess of Kent, she being a Princess of Greece and Denmark by birth. Another case concerns the late Princess Alice, Duchess of Gloucester, who was born Lady Alice Montagu-Douglas-Scott. Following the Duke's death she was allowed by HM The Queen to address herself as 'Princess Alice' (as opposed to 'Dowager Duchess'), a privilege granted to very few.
As for royal princesses who marry untitled individuals, the monarch can grant them titles such as in the cases of Antony Charles Robert Armstrong-Jones, who was created Earl of Snowdon upon his marriage to Princess Margaret, thus the princess becoming HRH Princess Margaret, Countess of Snowdon. If the couple chose not to accept a title, the wife then takes her husband's name but keeps her royal titles, eg HRH Princess Alexandra, The Honorable Lady Ogilvy, or if a total commoner, say if Princess Beatrice marries her boyfriend, and he is not granted a title, she will be HRH Princess Beatrice, Mrs Clark, but that is upon her own decision.
Now, it would be very different if the princess herself is the heir apparent.. say Prince George is followed by a sister and he someday chose to renounce his claim, then his sister would be the heir apparent to the throne. This will be a special case as princesses who are heir-apparent usually have their futures husband's title(s). Prince Philip was created Duke of Edinburgh when he married the then Princess Elizabeth but Philip was born a royal prince of Greece and Denmark, titles he renounced to become a British citizen in order to marry Elizabeth.
King George VI and the Queen Mother resented the fact that Princess Elizabeth was to marry a foreign prince as they wanted her to marry a British noble which from what i have read, possible candidates chosen by the King and Queen were William Cavendish, Marquess of Hartington, son of the 10th Duke of Devonshire (who later married Kathleen Kennedy, sister to President JFK); John Scott, Earl of Dalkeith later 9th Duke of Buccleuch; John Spencer-Churchill, Marquess of Blandford later 11th Duke of Marlborough and John Spencer, Viscount Althorp later 8th Earl Spencer (father of Diana, Princess of Wales) but the young Princess Elizabeth was was also said to be enamored by other highborn lords such as Hugh FitzRoy, Earl of Euston, later the 11th Duke of Grafton; Henry Herbert, Lord Porchester, later the 7th Earl of Carnarvon (also rumored to be Prince Andrew's biological father) and Patrick Plunket, later the 7th Baron Plunket.
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