If the Queen had not intervened, the new royal baby would be a lord or a lady, rather than a prince or a princess, and would not be an HRH.
Under past rules, only a first-born son of the Duke and Duchess of Cambridge would automatically have become a prince.
A Letters Patent in 1917, issued by King George V, limited titles within the royal family, meaning a daughter born to William or Kate would not have been an HRH but Lady (forename) Mountbatten-Windsor instead and a second-born son would also have lacked the HRH title and become Lord (forename) Mountbatten-Windsor rather than a prince.
The Queen issued a Letters Patent under the Great Seal of the Realm in December 2012 when Kate was around three months pregnant with Prince George, declaring “all the children of the eldest son of the Prince of Wales should have and enjoy the style, title and attribute of royal highness with the titular dignity of Prince or Princess prefixed to their Christian names or with such other titles of honour”.
If the new royal baby is a boy, he may be given a dukedom one day – most likely on his wedding day if he marries.
A girl might later in life, when William is king, have the honorary style the Princess Royal – which is currently used by Princess Anne. It is customarily given by the sovereign to his or her eldest daughter.
Day to day, the new addition to the royal family will be a Prince or Princess of Cambridge – following the dukedom given to William by the Queen on the morning of his wedding. William used Wales as his professional surname in the forces and his children are likely to use Cambridge in the same way.
Should the baby require a surname to get married or for legal reasons, it will be Mountbatten-Windsor.