I don't think so....
in reply to a message by Siri
It was a name long long before she entered onto the scene. I don't think Diana is any more too tied to the Princess than Elizabeth is to the Queen or Elizabeth Taylor. If a celebrity comes along with a name that did not exist or was not widely used before, such as Cher, Sigourney Weaver, or Miley Cyrus, then I can see saying it's too tied to the celebrity. But not in the case of a classic name like Diana.