Yes. If someone more famous than you appears with the same name, you can be told to stop using that name. At least online. (I dont cite to cnn often, but they were the first reasonable result when i googled around for the story.)
http://www.cnn.com/2011/WORLD/europe/01/25/kate.middleton.fa...
2011. "London -- Several Facebook users have had their profiles deleted from the social networking site because they share their name with a soon-to-be princess.
Kate Middleton, 33, from Melbourne, Australia, had her account shut down last week, after Facebook suspected her of pretending to be the fiancée of Britain's Prince William."