The name of the drug morphine takes its name from the Greek god Morpheus, the god of dreams and the illusions we see in sleep; his father is Somnus, the god of sleep. Friedrich Sertürner, a German pharmacist, isolated morphine around the year 1805 (it became commercially available in 1827), and he named it after Morpheus because the drug was sleep-inducing. You can read more at Wikipedia, and you can also read about the etymology of heroin in this post:
Heroine and Heroin.
The painting is a detail from
a fresco by Luca Giordano showing Morpheus and Night: