They're the names of the main men behind each game.
Hironobu Sakaguchi on ideas, Nobuo Uematsu on music, and Yoshitaka Amano on artwork and character designs. These three men are ultimately responsible for everything we know and love as "classic Final Fantasy." FFIX was their swan song.
In a parallel fashion, Yasumi Matsuno, Hitoshi Sakimoto, and Akihito Yoshida have had their own thing going for many years with games such as the Ogre Battle series, Final Fantasy Tactics, and Vagrant Story. Compared to the original trifecta, their vision is distinctly different but certainly equal in terms of sheer genius. Case in point: FFXII.