In the founding myth, even the town's name is linked to the goddess, as the eponymous Paphos was the son of Pygmalion and his ivory cult image of Aphrodite, which was brought to life by the Goddess as "milk-white" Galatea.

The author of Bibliotheke, the Hellenistic encyclopedia of myth long attributed to Apollodorus, gives the genealogy.

Pygmalion was so devoted to the cult of Aphrodite that he removed the statue to his palace and kept it on his couch.

The daimon of the goddess entered into the cult image, and the living Galatea bore Pygmalion a son Paphos and a daughter Metharme. Cinyras, perhaps the son of Paphus, but perhaps the successful suitor of Metharme, founded the city under the patronage of Aphrodite and built the great temple to the goddess there.

According to another legend preserved by Strabo, whose text, however, varies, it was founded by the Amazons.

If mythical time can be related to chronological time, this will have happened in the mid second millennium BC.