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 Co surname in historical dictionaries
Patronymica Britannica (1860)
in CO. Lancaster, formerly possessed by the CO. Wilts. AXON. Axton, a hundred in Kent. thorpe, CO. Rutland. CO. Warwick. CO. Norfolk. CO. Norfolk. Perhaps, sometimes the Germ. bote, a messenger. Ferguson thinks Botton, Botten, Botting, &c., modifications of the same word. CO. York, where the baronet's family resided temp. Hen. III. ston, CO. Leicester, or Congleton, co. Scoonic, CO. Fife. DURLEY. Parishes In Hants and CO. Salop (-where they still reside) by Edward the Confessor. The pedigree, however, is not traced beyond the time of Henry III. Sliirley's Noble and Gentle Men. CO. Sussex. IG GULDEN IGGLESDEN. See Bees, CO. Cumberland. It is also written Keenliside. At Stockton, co. Durham, it is corrupted to Kittliside, and at Newcastle to KittlcJiimside ! Paul, CO. Cornwall, anciently the residence of the family. C. S. Gilbert's Cornwall. CO. Worcester. CO. Sussex. CO. Northampton. The CO. Dorset. WEISTBORNE. A corruption of AVim