se legend gives answer.

* * * * *

When Heaven and earth were first created, there was neither Lake of Biwa
nor Mountain of Fuji. Suruga and Omi were both plains. Even for long
after men inhabited Japan and the Mikados had ruled for centuries there
was neither earth so nigh to heaven nor water so close to the Under-world
as the peaks of Fuji and the bottom of Biwa. Men drove the plow and
planted the rice over the very spot where crater and deepest depth now
are.

But one night in the ancient times there was a terrible earthquake. All
the world shook, the clouds lowered to the earth, floods of water poured
from the sky, and a sound like the fighting of a myriad of dragons filled
the air. In the morning all was serene and calm. The sky was blue. The
earth was as bright and all was as "white-faced" as when the sun goddess
first came out from her hiding in the cave.

The people of Omi awoke, scarce expecting to find either earth or heaven,
when lo! they looked on what had yesterday been tilled land or barren
moor, and there was a great sheet of blue. Was it sky? Had a sheet of the
"blue field of heaven" fallen down? Was it the ocean? They came near it,
tasted it. It was fresh and sweet as a fountain-rill. They looked at it
from the hill-tops, and, seeing its outline, called it "the lake of the
four-stringed lute." Others, proud of their new possession, named it the
Lake of Omi.

Greater still was the surprise of the Suruga people. The sailors, far out
at sea, rubbed their eyes and wondered at the strange shape of the
towering white cloud. Was it the Iwakura, the eternal throne of Heaven,
come down to rest on earth out of the many piled white clouds of heaven?
Some thought they had lost their reckoning; but were assured when they
recognized familiar landmarks on shore. Many a cottager woke up to find
his house, which lay in a valley the day before, was now far up on the
slope, with the distant villages and the sea visible; while far, far
above shone the snowy head of a mountain, whose crown lay in the blue
sky. At night the edges of the peak, like white fingers, seemed to pluck
the stars from the Milky Way.

"What shall we call this new-born child of the gods?" said the people.
And various names were proposed.

"There is no other mountain so beautiful in all the earth, there's not
its equal anywhere; therefore call it Fuji, (no two such), the peerless,
the matchless mountain," said one