Same way Jimmy is nickname for Vincenzo, Tommy for Gaetano, Johnny for Giovanni, Joe for Giuseppe. They just Americanized their names how they saw fit.
I wonder though why isn't it Vincenzo = Vincent and Jimmy/James = Giacomo. Theoretically, Vincenzo and Jimmy are 2 names with completely different origins.
I have no clue how they came up with Americanized names. Although Giacomo=Jack is pretty close in linguistics.
