Couve is a primarily French surname. Notable people with the surname include:
Adolfo Couve (1940–1998), Chilean artist and writer Jean-Michel Couve (1940–2025), French cardiologist and politician Maurice Couve de Murville (1907–1999), French diplomat and politician Maurice Couve de Murville (bishop) (1929–2007), French-born British Roman Catholic bishop Tomás Couve (born 1972), Chilean equestrian
See also Crécy-Couvé, a commune in northern France