She must change her name to become a princess
The honor of having the princess title is reserved for ladies born into the Royal Family. For example, Kate Middleton may be a duchess, but her daughter is Princess Charlotte. The only way for a royal bride marrying into the family to become known as “princess” is to use as the feminine version of her husband’s name. Diana was never officially “Princess Diana,” but was instead awarded that title by the media—and it stuck.
She was formally Diana, Princess of Wales. Meghan could use Prince Harry’s official title as a princess and would then be known as HRH Princess Henry of Wales, not “Princess Meghan.” Having spent over a decade in Hollywood before landing her big break and now that she’s starring in the world’s most popular soap opera, it’s highly unlikely Meghan would ever relinquishing her given name.