From the Greek ??, watchful. It may be derived from Gregor, as some of the Clan M'Gregor changed their name to Gregory, when the clan was proscribed and outlawed.

Arthur, William (1857) An Etymological Dictionary of Family and Christian Names. New York: Sheldon, Blakeman. Public Domain.

GREGORY. The well-known personal name has not onlj' become a surname, but has given rise to various others, especially Gregorson, Gregg, Gregson, Griggs, Grigson, Greig, Grix, and possibly Grocock. These forms are mostly Scotch, and Grier aud Grierson, not to mention Mac-Gregor, are cntirelj' so.

Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.