Ganymede was discovered by Galileo Galilei in 1610. The discovery, along with three other moons of Jupiter, was the first time a moon was discovered orbiting a planet other than Earth. Galileo's discovery eventually led to the understanding that planets orbit the sun, instead of our solar system revolving around Earth.
This was during the Renaissance when Italians were busy translating every Ancient Greek manuscript they could find. Greek myth was used to inspire paintings, sculptures, the naming of new discoveries and the early development of scientific language.
Jupiter was the ancient Roman name for the Greek god Zeus - the ruler of the Greek Pantheon of gods. Since a planet captures a moon by means of gravity, it seems Galileo considered the name Ganymede an appropriate metaphor.
Ganymede was a Trojan prince in Greek mythology. Zeus was notorious for his abductions and rapes.
"[Ganymedes] was the loveliest born of the race of mortals, and therefore the gods caught him away to themselves, to be Zeus' wine-pourer, for the sake of his beauty, so he might be among the immortals. — Homer, Iliad, Book XX, lines 233-235.