Unfortunately, I don't know any nicknames for my grandparents. I know that my grandfather Vincenzo's parents were Lorenzo Cannariato and Vincenza Falsone. My grandfather had 2 siblings: Francesca and Giorgio. Lorenzo came to the U.S. first, but was killed in an explosion while working on a road construction team. I believe he had 3 or 4 brothers.
My grandfather Vincenzo's mother, Vincenza Falsone, was the daughter of Giorgio Falsone and Giovanna Cutrano.
I visited Lorenzo and Vincenza's house in Prizzi years ago -- it was right next to an old church that I believe was no longer used.
I hope this helps!
Best wishes, Janet