Greenspan is a typically Ashkenazi Jewish surname. It is the anglicized form of the German/Yiddish surname Grünspan ("green swarf", "green patina", "verdigris", "copper(II) acetate"). Cognate are the surnames Grynszpan, Grinszpan and Grinshpan (Poland, Romania, Hungary).
Notable people with the surname include:
- Alan Greenspan (born 1926), American economist, former Federal Reserve Chairman
- Alison Greenspan (1972–2021), American film and television producer
- Ben Greenspan, American baseball coach
- Bennett Greenspan (born 1952), American entrepreneur, founder of Family Tree DNA
- Brad Greenspan (born 20th century), American entrepreneur (MySpace)
- Brian Greenspan (born 1947), Canadian lawyer
- Bud Greenspan (1926–2010), American film director
- David Greenspan (born 1956), American actor and playwright
- Dorie Greenspan (born 20th century), American author of cookbooks
- Edward Greenspon (born 1957), Canadian newspaper editor
- Harvey P. Greenspan (born 1933), American mathematician
- Herschel Grynszpan (1921-before 1945), Jewish assassin
- Jason Scott Greenspan (born 1959), aka Jason Alexander, American actor
- Jerry Greenspan (1941–2019), American basketball player
- Marshall Greenspan, American engineer
- Mauro Cabral Grinspan, (born 1971), Argentinian intersex and trans activist
- Melissa Greenspan (born 20th century), American actress
- Nachman Shlomo Greenspan (1878–1961), Polish-born UK rabbi and Talmudic scholar
- Natan Grinszpan-Kikiel, birth name of Roman Romkowski, state security official in Communist Poland
- Ryan Greenspan (born 1982), American paintball player
- Stanley Greenspan (1941–2010), American psychiatrist