At the current time, Prince William's ceremonial name and title in full is "His Royal Highness Prince William Arthur Philip Louis of Wales, Royal Knight Companion of the Most Noble Order of the Garter".
He is also styled " His Royal Highness Prince William of Wales"
As a British prince, William does not use a surname for everyday purposes. For formal and ceremonial purposes, Prince William has used the name of the area over which his father holds title, i.e. Wales (as Princess Beatrice and Princess Eugenie use York, per their father, Prince Andrew, Duke of York).
Prince William and Prince Harry are now using Wales as a surname in the military since they need one there.
When William marries, he, by convention, should be given a Dukedom. However, reports are that he asked his grandmother the Queen not to make him a Duke. He will automatically become Duke of Cornwall when (and if) he comes heir apparent. By convention, when he is heir apparent, he will become Prince of Wales, although this is not an automatic title.
If he is granted a Dukedom, or some lesser title as his Uncle Prince Edward was granted (Earl of Wessex), his formal title will become
H.R.H. Prince William, The Duke of ___________ (Cambridge, Sussex, or Windsor (which would be horribly tacky in my opinion) have all be mentioned.
Kate Middleton will become "H.R.H. The Duchess of ______________"
If he is not granted a peerage upon marriage, he will most likely continue to be styled "" His Royal Highness Prince William of Wales". Kate will probably be styled "Her Royal Highness Princess William of Wales".
However, for all practical purposes, she will be called Princess Catherine, or Princess Kate in the press.
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If all this sounds confusing, title and styles are granted by convention, precedence, and directly by the Monarch through the issuing of Letters Patent. Letters Patent trump everything, if The Queen wished that Prince William be called HRH Prince William, Adonis of the Universe that is what he would would be called formally -- if Letter Patent were issued to that effect. And they are taken very seriously.
The late Princess Alice, the mother of the Duke of Gloucester styled and titled "HRH Princess Alice, even though she was not born a Princess. This defied precedence, but it did not matter since Letters Patent were issued at the time.