Perhaps she went by her middle name or a sopranome? My grandfather was always known as Bruno - in fact, all the grandsons who were named after him were named Bruno but his real name was Francesco. No where on his birth certificate does it even say Bruno. Nonno's grandfather, Giuseppe had the same thing. His real name was Domenico - but on his children's birth records it listed him as Giuseppe. I finally obtained his death certificate and it says "Andriano, Domenico 'detto' Giuseppe"
I would try writing to the Comune in Firenze for the birth act and see what happens. You have nothing to lose. Have you his death act? You may also want to get that and the marriage act first just to see what's listed on them. It may actually list the place of birth and should list the parents names.