Hermaphroditus has a name that perfectly reflects those of his parents, Hermes and Aphrodite. He was, furthermore, a hermaphrodite, that is, he combined the physical characteristics of both sexes.
He was not originally so - he was born as a conventional baby boy - but became thus as a result of a total physical union (against his will, in fact) with the Naiad Salmacis when they embraced in a pool and their bodies joined together to form a single person (who had female breasts and proportions but male genitalia).
Hermaphroditus had been a handsome young man, however, and his name can be interpreted less anatomically, to imply one who had inherited the best characteristics (and especially the beauty) of both his parents. Socio-historians like to see his name as symbolic of the transition in Greek society from matriarchy to patriarchy.