|Could the third child's name be Benedetto? Ok.|
Also I can make out Rosaria (Ok) as Teresa Italiano's mother's given name but I can't seem to get the surname (maybe Agiola)
And I am assuming that the children belong to Nicolo and Teresa. (Yes) Was this a common practice to add such information to a marriage document later? Only when, such in this case, the parents were not married at the time of the child's birth. Or better: they were surely married, but only with a religious rite, and for the State their children were illegitimate. So, at the moment of the civil marriage, they declared to recogize the already born children like their legitimate and natural sons. This situation took place until 1929, when were signed the "patti lateranensi": after that date the religious marriage had also a civil value.