Derived from Middle English faie meaning "fairy". It appears in Geoffrey of Monmouth's Arthurian legends in the name of Morgan le Fay. It has been used as a given name since the 19th century. In some cases it may be used as a short form of FAITH.
Simply from the English word faith, ultimately from Latin fidere "to trust". This was one of the virtue names adopted by the Puritans in the 17th century.