Actually, Galileo only recorded sightings of THREE moons on this date; he found the fourth a few nights later. And those names were coined by the astronomer Simon Marius shortly after Galileo's discovery; Galileo named them for the four sons of his patron, the Grand Duke of Tuscany, and they were still called the the "Medicean Stars" as late as Cassini's tables of their movements. Marius' mythology-themed names did not become "official" until the twentieth century.