I'm an Italian national and I've just found out that have a second personal second name. However, when I was born, my parents separated it with a comma, which makes it legally invalid in Italy. This means that all my documents (passport, drivers license, marriage certificate, etc.) only have my first name.
The second name only appears on the notary act of birth.
Now I'm the process of applying for a green card and I'm wondering what I should declare since my second name is not legally valid in Italy.