Hades is indeed the Greek God of the Underworld. But don't confuse the Greek concept of the Underworld with the idea of Christian Hell. They are nothing alike. Hades and his wife, Persephone, preside over the souls of all of the dead as King and Queen.
But Hades is more than just the one who presided over the dead. He is much more complex than that. Check out the information about Hades at https://www.theoi.com/Khthonios/Haides.html