Diodati (given by God)

Amazing, we have the name “Diosdado” and until now I didn’t figure its origins.
BTW, do Italian women use their husband name when married?, and do you use your mother name?.
We use our first name, our father surname and our mother surname, that they keep using after married, only lately we can decide the order of our children second and third names.
Mine is an extreme case because my father is Juan Gil , my mother Maria Alexandres and me Juan Maria Gil Alexandres.