Clamp is a surname. Notable people with the surname include:
Arthur Clamp (1884–1918), English footballer Eddie Clamp (1934–1995), English footballer Paula Clamp (born 1967), novelist, playwright and Visiting Lecturer at the University of Ulster Shirley Clamp (born 1973), Swedish pop singer Steve Clamp (born 1976), British freelance journalist and newsreader Ted Clamp (1924–1990), English footballer William Clamp (1891–1917), Scottish Victoria Cross recipient