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.
Willie Marfeo to Henry Tameleo:
1) "You people want a loaf of bread and you throw the crumbs back. Well, fuck you. I ain't closing down."
2) "Get out of here, old man. Go tell Raymond to go shit in his hat. We're not giving you anything."