The Queen has been pleased to declare Her will and pleasure that Her Royal Highness Princess William of Wales shall henceforth be known as Her Royal Highness The Princess Catherine.
She would not be The Princess Catherine as this is reserved for the children of the monarch. But the Queen could create her or allow her to use the style of HRH Princess Catherine like she did with Princess Alice, (Dowager) Duchess of Gloucester. There has been no other example as HRH Princess Marina, (Dowager) Duchess of Kent was a princess born and HRH The Duchess of York became HM Queen Elizabeth and later HM Queen Elizabeth, the Queen Mother, while the Duchess of Windsor never was accepted as a princess.
Personally I don't think we can guess what HM is thinking about this and what she will do. During her long reign she has seen a lot of changes in society and in her own family. She has seen how her parents treated her uncle, a former king and his wife, who was a divorcee, she has allowed to present divorcees at her court, seen her sister and three of her children file for divorce and her heir marry a divorcee without loosing his place in her family and her succession.
She stripped her two daughter-in-laws of their HRH-styles, which for her (think about the Windsor-title-drama) surely was the right thing to do for her considering the past but turned out to be to no avail for the people and the media of the UK. They still spoke and wrote about "The Duchess of York" and "Princess Di" as if nothing had happened. As nothing really had happened, for most people HRH is simply a style, but nothing you use in ordinary life when referring to a person.
Then there is the example of Denmark. Alexandra after her divorce was stripped of her HRH as well, but got the HH-style while keeping the name of a princess till she remarried, then using her own title of a Countess. Thus she was firmly put in her place while at the same time she was recognized for what she had been and what she became on her new marriage.
So I wouldn't wonder if HM tried out something else this time: on allowing Catherine to use the style of HRH Princess Catherine, Princess William of Wales or The Duchess of X, she shows the world who Catherine is now - second-in-line to become Queen consort. But in case of a divorce, she could simply stop allowing her to use that style and bestow a different style/title without Royal references for future use after the divorce is final.
Which would be something people understand much easier than the fact that there was a difference between The Princess of Wales (known to most as Princess Diana) and Diana, Princess of Wales. When former "Princess Catherine" is suddenly known as Baroness Catherine or Lady Catherine, people would notice that the former princess is no longer one.