In part from the English word
fay meaning
"fairy", derived from Middle English
faie meaning "magical, enchanted", ultimately (via Old French) from Latin
fata meaning "the Fates". It appears in Geoffrey of Monmouth's chronicles in the name of
Morgan le Fay. In some cases it may be used as a short form of
Faith. It has been used as a feminine given name since the 19th century.
As a rarer (but older) masculine name it is probably derived from a surname: see Fay 1 or Fay 2.