Phoebe was a popular name, being that of a Titaness, the daughter of Uranus and Gaia, of a daughter of Leucippus, and of a daughter of Tyndareüs and Leda, among others. It means 'bright', 'pure', 'radiant' (phoibos), which is obviously a good name to have.

Note that the Titaness married her brother Coeüs, whose name could be interpreted as 'lucid' (see his name). Phoebe was also a by-name of Artemis in her capacity as goddess of the moon. In this respect see the name of Leucippus' other daughter, Hilaira.