Taken from the Internation Movie Database (IMDb) about Fûinaru Fuantajî - Final Fantasy (1987):
Hironobu Sakaguchi called his game "Final Fantasy" because he intended it to be his last game before leaving the industry.
Weird, isn't it? He intended to quit in 1987, but he's still working on the series now in 2004.
Source: http://www.imdb.com/title/tt0207484/trivia