Fynes is a given name. Notable people with the name include:
- Fynes Moryson (or Morison) (1566–1630), travelled in the 1590s on the European continent and the eastern Mediterranean lands
- Henry Fynes Clinton (1781–1852), English classical scholar and chronologist, born in Gamston, Nottinghamshire
- Savatheda Fynes (born 1974), track and field sprint athlete, competing internationally for Bahamas