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.
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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.