This is her 'occupation' or 'job description', and does not mean she should be addressed as Princess. On marriage to Prince William, she became Princess William of Wales – in the same way that the wife of the Queen's cousin Prince Michael of Kent is Princess Michael of Kent.
Since her wedding Kate has been styled HRH the Duchess of Cambridge
On marrying direct descendents of the monarch are typically given a dukedom or, in the case of a younger son they become an Earl. William became the Duke of Cambridge, meaning his wife is entitled to be known as Her Royal Highness the Duchess of Cambridge.
This is why his uncles Prince Andrew and Prince Edward are the Duke of York and the Earl of Wessex respectively. Prince Harry when he marries can expect to be honoured in a similar fashion.
This derives from the title the Queen gave her husband on their marriage
When in due course his brother becomes King, Kate will become Queen Consort.
The paperwork for George was filled out by hand by Alison Cathcart, the deputy registrar of Westminster who visited William at Kensington Palace. She described it as “a great pleasure” and privilege.
She said: “We also registered the birth of the Queen and Prince Charles and Princes William and Harry, so it’s great to see that tradition continue.”
The certificate does not give a surname for the new mother.Members of the royal family usually do not need a surname.
Prince George's birth was registered at Kensington Palace on Friday
If for any reason one is required the Queen's children or grandchildren can be known as Mountbatten-Windsor – the surname of the sovereign's husband Prince Philip plus the name of the royal house. Princess Anne when she married listed her last name as Mountbatten-Windsor.
Another option is a surname associated with their title. William when he is on duty as a search and rescue pilot is known as Flight Lieutenant William Wales – apparently giving rise to the nickname Billy the Fish among his work colleagues.
His cousin Princess Beatrice of York called herself Beatrice York at university.
Royal titles explained:
King and Queen:
If the monarch is a man he is referred to as a King. A woman can be a Queen in her own right as in the case of Queen Elizabeth or because of her marriage to a King, which will be the situation with Kate Middleton.
The spouse of a Queen usually becomes a Prince. In Prince Philip's case he was a Prince of Greece. Before his marriage in 1947, he became a naturalised British subject and dropped his Greek royal status, becoming the Duke of Edinburgh. In 1957, his wife bestowed on him style and title of a Prince of the United Kingdom.
Duke and Duchess:
This is a title ranking just below a monarch. There are royal Dukes who are members of the reigning house and Dukes outside the family, for example the Duke of Westminster.
Prince or Princess:
This is a title inherited through male descendents. For example, the children of Princess Anne are not Prince or Princess. Using their father's name, they are known as Zara Phillips and Peter Phillips.
You can be a Princess and not use the title. Camilla, the Duchess of Cornwall is technically the Princess of Wales out of respect for the late Diana, Princess of Wales she has never used that title. Instead she uses her husband Prince Charles' Dukedom.
In 1917 George V changed the name of the royal house to Windsor from the German Saxe-Coburg- Gotha – the surname of Queen Victoria's husband because of World War I. Later the Queen and Prince Philip added his name Mountbatten for their children and grandchildren.