Technically speaking, Catherine, Duchess of Cambridge, already has a princess title: she "shares" her husband's title and could, correctly, be called Princess William, Duchess of Cambridge. But that's a form that's rarely used, and it's not a title that combines her own name with a princess title.
That will change once Charles is king and William is Prince of Wales. At that point, Catherine will be styled as Catherine, Princess of Wales. Calling her "Princess Catherine," however, would still be incorrect: the style "Princess" first name is reserved only for the daughters of monarchs or princes, like Princesses Anne, Eugenie, Beatrice, and Charlotte. However, the media and the public often referred to Diana as "Princess Diana" and we can probably expect the same for Catherine.