A few more:

Vincenzo - Vincent or Vinny
Gaetano - Thomas or Tommy or Tom
Eugenio - Eugene or Gene
Michele - Michael or Mike or Mickey
Michelangelo - Same as Michele
Donato - Donald or Donnie or Don
Donatello - Same as Donato
Raffaele - Ralph or Ralphie
Leonardo - Leonard or Lenny, or Leo (I guess we could argue that Leo is still Italian)
Davide - David or Dave
Beniamino - Benjamin or Ben or Benny
Gennaro - Gerald or Gerry or Genny
Gerardo - Gerard or Gerry