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Last name origins & meanings:

1. Cornish and Welsh: nickname for a red-haired man, from cough, coch ‘red(-haired)’. Compare Gough.
2. English: metonymic occupational name for a maker of beds or bedding, or perhaps a nickname for a lazy man, from Middle English, Old French couche ‘bed’, a derivative of Old French coucher ‘to lay down’, Latin collocare ‘to place’.