Costin is both a Romanian and English surname and a given name. Notable people with the name include:
Surname:
- Brandon Costin, Australian rugby league player
- Darren Costin (born 1966), English musician
- Doug Costin (born 1997), American football player
- Frank Costin (1920–1995), British automotive engineer
- Gheorghe Costin (born 1955), Romanian conductor and composer
- Henry Gilbert Costin (1898–1918), United States Army soldier and Medal of Honor recipient
- Ion Costin (1887–1940), Moldovan politician
- Jamie Costin (born 1977), Irish racewalker
- Mike Costin, British automotive engineer
- Miron Costin (1633–1691), Moldavian chronicler
- Nicolae Costin (1936–1995), Moldovan politician
- Nicolae Costin (chronicler) (1660–1712), Moldavian chronicler
- Raul Costin (born 1985), Romanian footballer
- Robert Costin, British classical organist, teacher and conductor
- Sergiu Costin (born 1978), Romanian footballer
- Thomas P. Costin Jr. (born 1926), American politician
- William Costin (c. 1780 – 1842), early American civil rights activist in Washington, D.C
Given name:
- Costin Alamariu (born 1980), Romanian-American writer and an internet personality
- Costin Curelea (born 1984), Romanian footballer
- Costin Gheorghe (born 1989), Romanian footballer
- Costin Lazăr (born 1981), Romanian footballer
- Costin Miereanu (born 1943), Romanian-born French composer and musicologist
- Costin Nenițescu (1902–1970), Romanian chemist
- Costin Petrescu (musician) (born 1949), Romanian rock musician
- Costin Petrescu (painter) (1872–1954), Romanian painter