While the name of the Bocchiccios is never mentioned in any of the films, there is a reference made to them in GFI by Clemenza, right before Michael goes to the meeting with Sollozo.
TOM
What about the negotiator?
CLEMENZA
He's over at my place playin' pinochle with a couple of my men. He's happy, they're lettin'
him win...
TOM
There's too much of a risk for Mike -- maybe we outta call it off, Sonny.
CLEMENZA
The negotiator keeps on playing cards until Mike comes back safe and sound.
Yes, the actual name 'Bocchiccio' is never used in the film, but the families DID use a negotiator. Assumably The Bocchiccios.
Don Cardi
