Diana was HRH the Princess of Wales before her divorce and Diana, Princess of Wales after the divorce. The latter was a negotiated title, acknowledging that she had royal sones but stripping her of personal royalty (the HRH) If you are non royal and want to use the title of Princess, you have to lose your own name and use your husbands (like Princess Michael of Kent)
There seems to be goss that it was deemed "unwise" shall we say for William's wife to have a better title than her father in law's wife. Of course, she may also have had a preference, like Princess Anne not wanting to be the Princess Royal while she was still competing as a showjumper.