What was Kirito's actual family name? Most of you will say Kirigaya, but that is his adopted family name.  Kazuto's mother was Midori's sister and was married to a man from a different family.
Per the fan wiki, his surname was Narusaka (鳴坂) prior to his adoption.


  Born on October 7, 2008, Narusaka Kazuto was adopted by his aunt and uncle a year after his birth, when his biological parents died in an accident.


According to this news article and some other sources I found, this was revealed at the beginning of Unital Ring, originally in the January 2018 issue of Dengeki Bunko, which publishes SAO as a serialized story.