Since J is a very uncommon letter for Italian names, I wasn’t able to find more than a handful for today.
Jacobella (T) is an elaborated feminine form of Jakob. Though the traditional meaning for this name (whose original Hebrew form is Ya’akov) is “heel, supplanter,” many modern linguists and Biblical scholars now believe that was a folk etymology. Instead, the name may come from Semitic roots meaning “may God protect.”
Junipera (I) means “juniper.”
Jacobello (I) is an elaborated form of Jakob, as explained above. This was also used as a nickname.