Why is the underworld called the underworld despite the fact that is in a world that is underground?

It is below any other realm, so it is UNDER the rest of the WORLD.

To the Greeks, the world was a flat disk with the Heavens above, Okeanos the world sea all around, and Hades below. Just remember the distinction of Hephaestos' forge being underground, i.e. within the earth, and Hades being below or under the earth; a whole realm unto itself, rather than just a cave.