Ganymede was the son either of Tros, the founder of Troy, or of Laomedon, the father of the Trojan king Priam. He was a beautiful boy, and according to Homer was abducted by the gods to live as a cup-bearer to Zeus.
His name may well not have been Greek originally, but it must have suggested to a Greek ear ganos, 'beauty', 'delight' and medos. The latter word was used only in the plural (medea) as which it could mean either 'plans', 'cunning' or 'genitals' (in which sense it corresponded to Latin virilia).
So his name means either 'delighting in cunning', or 'rejoicing in manhood' (i.e. in his own prospect of marriage), or even 'with delightful genitals'. (One hardly suspects that the gods abducted him for his cunning.)
His name, in a rather perverse form, gave the Latin Catamitus which in turn produced the English 'catamite' as a word for what Chambers Twentieth Century Dictionary somewhat quaintly calls 'a boy kept unnatural purposes'.