According to the Etymology dictionary, the word priapism comes from Priapus son of Dionysus and Aphrodite, the god who personified male reproductive power. His name is of unknown origin". He was a minor rustic fertility god, protector of livestock, fruit plants, gardens and male genitalia. Priapus is marked by his absurdly oversized, permanent erection. He became a popular figure in Roman erotic art and Latin literature, and is the subject of the often humorously obscene collection of verse called the Priapeia, in words of wikipedia.
Other words referring to priapism are : priapic and priapulid. We can see the use of the word in this article