My full name is Giacomo but everyone calls me Jake or Jack; especially when I'm in an English speaking country. I don't like "James" used for Giacomo: It sounds so different from the original version of my name. Jim or Jimmy are also so far from my original name and I dislike them. In Italian as nicknames for Giacomo we have: Giacomino, Giaco, Giachi and Mino. Giacobbe and Jacopo are another forms of Giacomo, because they have the same etymology and the same meaning.
https://lij.wikipedia.org/wiki/Giacomo_Devoto
https://lij.wikipedia.org/wiki/Giacomo_Fregoso
https://lij.wikipedia.org/wiki/Giacomo_Grimado_Dua%C3%A7o
https://lij.wikipedia.org/wiki/Giacomo_Lomellin