I know that story about the name of the kid actor being Anthony and he responding better when called by his real name is true, but what Sicilian Babe says makes a lot of sense.
I think the FFC and the production noticed the actor responding better when called Anthony, and since it fits fine in the family context, they used it.

A Question: In GF1, we don't hear any quotation to Vito's father. (at least I don't remember) But does the novel tells anything about him? if it does not, this grandfather-great gandfather thing didn't have any influence