It is a Cornish name thought to have derived from Cornish "cough" (red) and to have been a nickname for a redheaded man (the usual Cornish pronunciation is "cooch").
The Cornish surname appears in 1160 as "Coh" and over the centuries as "Coch," "Cogh," "Cooch," "Cough," "Cuche," "Cowche," "Cowtch," "Coutch," etc., until the spelling became standardized in recent centuries, generally as "Couch.
"[1] There is also an English name Couch which probably originated as a name for a maker of beds or bedding.
[2] The English surname has variant forms Coucha, Couche, Coucher, Couchman and Cowcha.
[2] Notable people with the surname include: