I think Edward is a better name and Eddie should be a nickname. Edward might be the name of Edward Cullen but it is still is a nice name.
Eddie Rickenbacker's name was Eddie Rickenbacker.
Eddie Schumacher's birth name is Eddie Schumacher.
Eddie Vartan's birth name is Eddie Vartanian.
Eddie Alfano's birth name is Edward J. Alfano.
Eddie Mabo's birth name was Eddie Koiki Sambo.
Eddie Underwood's birth name is Eddie Paul Underwood.
Eddie Peregrina's birth name is Eddie Villavicencio Peregrina.
Eddie Watt's birth name is Eddie Dean Watt.
Eddie Michel's birth name is Eddie Michel Azoulay.
Eddie Imazu's birth name is Eddie Yasuhei Imazu.
Eddie Cruse's birth name is Eddie Dean Cruse.
Eddie Karnil's birth name is Eddie Edvardo Karnil.