As many of them appear to have nicknames, at least to us, this might come as a surprise. Inside the Royal Family, everybody is known by their full given name. We have a habit of referring to the Duchess of Cambridge as 'Kate Middleton', 'Princess Kate' or 'Duchess Kate', but that's not how she refers to herself, and nor is it how her husband refers to her. She's called 'Catherine'.
In the same way, despite the fact that he and his brother have been termed 'Wills and Harry' by the press since they were born, Prince William has only ever been 'William' at home. This extends to the rest of the family. The Queen, nor any of the other Royals, will have used the terms 'Princess Di' or 'Fergie', and Heaven help you if you were ever to call the Queen 'Liz'.