Priapus was a Phrygian god of fertility, and was associated with gardens, vineyards and agriculture generally. He was borne by Aphrodite to Dionysus or Hermes, and was represented as an ugly scarecrow-type man with huge genitals. The origin of his name is obscure.

Attempts have been made to link it with prio, 'to saw', this being a reference to his gardening activities as a pruner of trees, and Robert Graves sees him specifically as a 'pear-tree pruner', from prio and apios, 'pear-tree', this being a tree sacred to Hera.

One theory refers to the by-name Briepyos used of Ares by Homer in the Iliad, this meaning 'shouting loudly' (from bri-, an intensive prefix, and epyo, 'to shout'), and maintains that Priapus' name was originally something like 'Briapus' with this same sense.

All the evidence points to his name being at any rate erotic or phallic in some way, resembling the senses of the names of other phallic deities such as Orthanes ('erect'), Conisalus ('dust whirler') and Tychon ('he who hits his mark'). If Hermes was his father, then here is another phallic link. Maybe after all Priapus originated as an orgiastic by-name, whatever its meaning, of Dionysus.

Understandably, the name has not passed on to any heavenly body, nor has it become a personal forename. Its only use is as a medical term, 'priapism', to refer to a persistent erection of the penis. This word derives from the Greek verb priapizo, 'to be lewd', 'to be like Priapus', which itself came from his name.