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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The Cotes surname in historical dictionaries
Patronymica Britannica (1860)
COTES. A manor in Stadordshire gave name to this family, who are " descended from Richard de Cotes, probably the son of Thomas de Cotes, living in 1167, when the Black Book ofthe Exchequer was compiled. About the reign of Henry VI. the family removed to Woodcote in Shropshire, which has since continued their principal seat, though the more aucieut manor of Cotes or ' Kotes,' on the banks of the Sow, has ever remained the property of this aucieut house." Shirley's Noble and Gentle Men.