Arthur, William (1857) An Etymological Dictionary of Family and Christian Names. New York: Sheldon, Blakeman. Public Domain.
COX
As described in historical dictionaries
An Etymological Dictionary of Family and Christian Names (1857)
Cock, little--a term of endearment, a diminutive, the same as ot or kin, used as a termination, as Willcox, little Will; Simcox, little Sim, etc. The word is also often used to denote a leader or chief man. Addison says: "Sir Andrew is the cock of the club."
Patronymica Britannica (1860)
COX. COXE. See Eng. Surn. under Cock, i. 165. Probably a sjaionym of Little. It may, however, be the same as Cook, from its latinized form, thus : Cocus, Cocks, Cox.
Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
Surname type: Nickname
Origin: English
Region of origin: British Isles
Country of origin: England
Religion of origin: Christian
Language of origin: English