Origin: Latin, Gaelic
Meaning: derived from Latin fata (destiny, fate) meaning "fairy" or "elf, sprite".
Fay is also a place in France derived from Latin fagus meaning "beech tree".
Fay was also a now obsolete word originally meaning "faith" or "loyalty" from Old French; incidentally, Fay could also be a nickname for the name Faith from Latin fidere meaning "to trust", or for Francis/Frances meaning "Frenchman".
Spelled Fey, it's related to a Germanic word meaning "fated to die".
Fay is also a Gaelic surname from Fahey, an Anglicized form of Ó Fathaidh or Ó Fathaigh meaning "descendant of Fathadh", from a personal name meaning "base" or "foundation".