Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
COCK
As described in historical dictionaries
Patronymica Britannica (1860)
COCK. The bird — corresjonding to the Lat. Gallus, the Fr. Le Coq, Cochet, Coquerel, the Germ. Hahn, &c. Sometimes it was as probably a sobriquet applied to a diminutive person. See Cock, below.