Mount Parnassus is named after Parnassos, the son of the nymph Kleodora and the man Kleopompous. There was a city of which Parnassos was leader, which was flooded by torrential rain. The citizens ran from the flood, following wolves' howling, up the mountain slope. There the survivors built another city, and called it Lykoreia, which in Greek means "the howling of the wolves
As the Oracle of Delphi was sacred to the god Apollo, so did the mountain itself become associated with Apollo. According to some traditions, Parnassus was the site of the fountain Castalia and the home of the Muses; according to other traditions, that honor fell to Mount Helicon, another mountain in the same range. As the home of the Muses, Parnassus became known as the home of poetry, music, and learning.
Parnassus was also the site of several unrelated minor events in Greek mythology.
Parnassus of Raphael
Parnassus as metaphor
The name "Parnassus" in literature typically refers to its distinction as the home of poetry, literature, and learning. Thus, it receives mention in such works as the Parnassus Plays (referring to the University of Cambridge); Christopher Morley's Parnassus on Wheels (referring to a mobile bookseller); and the "New Parnassus," the salon of Marguerite of Navarre. In Edward Albee's play "Who's Afraid of Virginia Woolf," Parnassus is also mentioned in this manner.
MAPS of Modern Greece from Hellenic Republic - Ministry of Tourism - Greek National Tourism Organisation