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