The Ancient Greeks did have some marvelous names and many of them are popular today with the Kardashian-endorsed Penelope, Cassandra, Echo, Athena and Persephone (at least in the blogosphere) but Aphrodite (pronounced a-fra-DIE-tee) has never been endorsed as a baby name. I think though that it has more to do with the myth surrounding the iconic figure rather than anything else.
She is often depicted as vain, ill-tempered and easily offended in later myths and she is actually one of the few Greek Gods and Goddesses to actually be married, though that doesn't stop her having affairs. I wouldn't see this as a deterent to using the name. Plenty of babies are born to the name 'Scarlett' after Scarlett O'Hara in Gone with the Wind, and though I love the character, she could easily be described as having these attributes as well.
Aphra also makes for an interesting nickname for her (or could even be another choice for a baby name if you don't want to outwardly state your love of Aphrodite) and that name has a positive role-model in the form of 17th century writer, Aphra Behn, the first woman in England to be a published author.
Aphrodite is one of those names that falls into the lines of Bathsheba, Cleopatra and Neferiti I suppose as infamous beauties of their time that need no other name but then all your have to say is Monroe and everyone automatically thinks of Marilyn Monroe and plenty of people are calling their child after her, and that is definately a big thing for little girls to grow up into. It might be seen as famous for one namesake but it isn't until others start to use the name as well that it will be seen as just a name - a rather beautiful name.