The actor who plays Edward in real life doesn't have the name Edward. In real life his name is Robert Pattinson. In the Movies and book is name is Edward Cullen, but before he became a vampire his last name was not Cullen.
The actor's name is Robert Pattinson. Edward's name in the book is Edward Anthony Masen Cullen, Masen being his original surname when he was human. Edward was also his father's name.