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
• 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 (born 1941), 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 (born 1941), American psychiatrist