Who is the Greek god of sleep?

The Greek god of sleep is Hypnos.

Hypnos is the personification of sleep in Greek mythology, and his name became the root of modern words such as “hypnosis” and “hypnotic.” In Hesiod's Theogony, he is one of the offspring of Nyx, the goddess of Night. Some later genealogies name Erebus, Darkness, as his father. Hypnos is commonly paired with his twin brother Thanatos, the personification of death.

Myths place the brothers in the Underworld or at the far edge of the world, near the realm of dreams. Hypnos appears prominently in Homer's Iliad, where Hera persuades him to lull Zeus to sleep during the Trojan War. Hypnos is initially reluctant because Zeus had previously chased him in anger after an earlier deception, but Hera promises him marriage to Pasithea, one of the Charites.

Artists often portray Hypnos as a winged youth, sometimes carrying sleep-inducing plants or pouring water associated with forgetfulness. He is easily confused with Morpheus, who shapes dreams, and Thanatos, who represents death; neither is the general Greek personification of sleep.