Nicknames are a no-go.
The real name of Kate Milton is actually “Catherine Elizabeth Mountbatten Windsor,” which means that we obviously call her by her nickname that is Kate Milton. This is an odd case in the royal family, especially when married. The royal family lives up to keep things formal, not leaving behind their names, and everybody after getting married into the royal household is given a new name.
Although Meghan Markle’s name is Rachel, she is still known as Meghan, the Duchess of Sussex. It’s not new for the Royals to have things their way, which may appear sometime to be unusual for us commoners. It also alludes to another interesting point to note that perhaps a lot of thought the process goes into what names will Royals be called as in the public.