Diana correct name was Princess Charles but wouldn't have been used as she would have been know as HRH P o W. as she wasn't a royal in her own right only by marriage.
Her Royal Highness The Princess of Wales and Countess of Chester, Duchess of Cornwall, Duchess of Rothesay, Countess of Carrick, Baroness of Renfrew, Lady of the Isles, Princess of Scotland.
It was the press and public that named her Princess Diana.
Prince William Arthur Philip Louis
Prince Henry (Harry) Charles Albert David