Oh, Stephie, why did you have to put shame on a beautiful name that had already been chosen by much better authors than you?
There are better characters named Edward than Edward Cullen, of course. Here are some examples:
1) All real life Edwards ever
2) Edward Rochester (Jane Eyre)
3) Edward Elric (FullMetal Alchemist)
4) Edward Scissorhands
5) Prince Edward (Enchanted)
6) Edward Ferrars (Sense and Sensibility)
7) Edward Mars (Lost)
8) Edward Chris von Muir (Final Fantasy IV)
9) Ed, Edd n Eddy (they're funny!!!)
10) Edward Bear (aka teddy bear aka Winnie the Pooh)
11) Edward Teach (Pirates of the Caribbeans)
12) Edward Nigma a.k.a. The Riddler (Batman) "Riddle me this; I claim to be a vampire and dangerous(but I'm not), and my hobbies involve stalking my girlfriend and being an abusive control freak. Who am I?"
13) Edward Kenway (Assassin's Creed IV: Black Flag)
14) Edward the Blue Engine (Thomas the Tank Engine and Friends)
15) Edward Malone (Conan Doyle Books). Like Edward Cullen, he became infatuated with the wrong person. Unlike him, he eventually grew out of it.