"How do we write her surname?"
Translation:Come scriviamo il suo cognome?
Verbs already contain the subject in them so that io, tu, lui, lei... don't need to be expressed.
This implies that when you use the personal pronoun as a subject, then you put extra emphasis on it.
So adding noi here would be like saying 'how do we, and not you, write ...'
Come si scrive = how does one write (this word, the famous person's name...)
Come scriviamo = how do we write (this word, the famous person's name...)
Come ci scriviamo = how do we write (to one another, for one another...)
Pronouns are pretty complex because they rarely follow one single rule. Sometimes just getting used to the way they work is more effective than memorizing lists of rules.
Oh, now that makes Sense! I have been baffled by this because I did not use il mio figlio or il mia sorella and git it correct, but this called for a 'il" because it belongs to many people (cognome), not singular, but more like a plural. Is my reasoning correct??? But how about "il mio nome"; would that be correct as well?
Possessives in Italian are like all other adjectives. They must agree with the noun they go with. "il cognome" is masculine, so all modifiers that go with it must be in masculine form, including possessives. It doesn't matter whose it is.
This has been discussed on this page before.