Susano-o-no-Mikoto did not come strictly as an emissary of his pantheon, but the gods of Japan were expanding, and they felt that Hell should belong to them. He offered whatever price that Dream asked. In the end, he left after Dream found for an other supplicant.
Traditionally, Susano-o-no-Mikoto is the god of storms, thunder, and seas.
He is later seen in the spin-off series, Lucifer, in a larger role.