yup, his full name is edward anthony mason cullen. Edward- he was named after his dad (edward mason sr.....Anthony-not really sure were that comes from...... Mason-that comes from his mother(elizebeth mason, who died from the spanish influenza, her death wish being that carlisle save edward jr in any way he can).... And cullen is from his "adoptive" father/mother( for all intensive purposes) carlisle & esme cullen, whom are in no way related to, besides the fact that they are all vampires.
Edward's full name is Edward Anthony Masen Cullen. So now that he's a Cullen, his middle name is probably Masen. I got this from the card toi get from the soundtrack.