Regarding the recent discussion of possible future changes to the system of royal titles... I don’t believe we know the Prince of Wales’s opinion of gender discrimination in titles, but there has been some indication that he might want female consorts to use their own forenames instead of their husbands’.
His views may have evolved since 2011 and may further evolve by the time he becomes King, and it is possible that the leaks in 2011 misrepresented his views in some manner, but for whatever it is worth:
When the then Prince William of Wales was engaged to be married to Catherine Middleton, he allegedly wanted his wife to be called Princess Catherine. Queen Elizabeth II allegedly denied his alleged request.
Nonetheless, William allegedly felt so strongly about his alleged wishes that he had his spokesman issue a statement – on the record, not “allegedly”. This statement (which I’ve bolded below) was interpreted by some royal watchers as not-so-subtly encouraging the public to colloquially refer to his wife as “Princess Catherine” even though her official title on marriage was HRH The Duchess of Cambridge.
December 12, 2010:
“"He says he was born Prince William and wants to continue to be known as that," says a courtier. "He wants Kate to become Princess Catherine."”
April 29, 2011 (wedding day):
“Explaining the slightly confusing picture, a palace spokesman said: "She is not a princess in her own right. That title has not been conferred on her. Her title is that of duchess. So she is not Princess Catherine. And to call her Princess William of Wales is misleading."”
Queen gifts grandson highest rank in British peerage, meaning Kate Middleton will not officially become a princess
www.theguardian.com
May 1, 2011 (two days after the wedding):
“Although the Prince's spokesman said he was "honoured" to become the Duke of Cambridge, he had let it be known that he would prefer to remain Prince William and for his wife to become "Princess Catherine".
[…]
In an attempt to get round the issue, the Palace let it be known that people who wanted to call Catherine "Princess" were welcome to do so.
After Friday's Royal wedding, Paddy Harverson, the Prince of Wales' communications secretary, suggested the public be encouraged to use the names Prince William and Princess Catherine if they preferred.
He said: "I think it's absolutely natural that the public might want to call them Prince William and Princess Catherine and no one is going to have any argument with that."”