There are a lot of great names that have their roots in Greek mythology. Some names of Greek myth are still commonly used like
Artemis,
Athena, Jason,Iris, etc. But I would definitely want to know the myth surrounding the name before I used one. For instance,
Jocasta unwittingly married her son
Oedipus. She commits suicide when she learns that he was her son.
Some other names from Greek myth:
Girls:
HeraCirce MedeaDemeterThaliaEuphrosyneCallypso
NikeElectraClioCalliopeHelenDioneHecateLigea
PallasPersephoneAsteria
TheiaAriadne
Boys:
TheseusHectorMarsyas - he was flayed...
Thespias
Chiron
CastorArcas
Xanthus
PanAristaeus