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English: habitational name from any of numerous places called Coates for example in Cambridgeshire Gloucestershire Lincolnshire Nottinghamshire Shropshire Sussex and Wiltshire; Cotes in Leicestershire or Staffordshire; or possibly from Coat in Somerset Cote in Oxford and Yorkshire with excrescent -s; or possibly from any of numerous other places similarly named from the new Middle English plural form cotes of Old English cot (plural cotu) ‘cottage’ also ‘shelter’ and sometimes ‘woodman's hut’. It is possible that some bearers may be from a place whose current name is from the dative plural form of this word cotum for example Coatham (Durham) or Cottam Cotham (Nottinghamshire) or from the plural of the related weak noun cote plural coten. Cotham (Nottinghamshire) is early recorded as Cotes and Coton (Cambridgeshire Derbyshire Northamptonshire) have many similar spellings. See also Coate . There are very small places in Midlothian East Lothian and Fife called Coates but the surname seems rarely if ever to be Scottish in origin. Americanized form of German and Jewish (Ashkenazic) Kotz or perhaps German Koths .
Source: Dictionary of American Family Names 2nd edition, 2022