See the link below regarding Italian heraldry. Your reponder is correct. They were/are granted to individuals not families. The surname product business is a big scam.
When surnames were taken or assigned in Europe during the last millennium it wasn't impossible for legitimate sons of the same man to wind up with a different surname and still each could have shared his with others with no known relationship. The purpose was not to identify a man as a member of a family but just to better identify him, frequently for taxation purposes. Too many men with the same given name in the same town or village and they had to hhave a way of sorting them out. Surnames were just "words" that had a way of identifying a man such as indicating he was the son of another, his occupation, where he lived or some characteristic of description of him.http://www.regalis.com/onom.htm