Tityus was a giant, said to be the son of Zeus and either Gaia or Elare (the daughter of Orchomenus). He is chiefly known for his attempt to rape Leto. For this offence he was taken to Hades and stretched helpless on the ground while two vultures ate his liver, which grew again with each new cycle of the moon.
The liver was the supposed seat of lust, and if Tityus is regarded as a kind of personification of lust, his name can be seen as a reduplication of thyo, 'to rush on', 'rage', such a reduplication resembling those considered for Sisyphus and Tantalus. There certainly seems to be something phallic or erotic in his name even if one derives it instead from titycomai, 'to prepare', 'aim at'.