Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
We don't have any stats on how common this name is. This is probably because it's very rare in the UK.
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Related and similar surnamesCocks
The Coxe surname in historical dictionaries
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.