The Galilean Moons (Voyager Images)
Io, Europa, Ganymede and Callisto

Simon Marius claimed to have observed Jupiter's moon as early as late November 1609 (about five weeks prior to Galileo) and had begun recording his observations in January 1610 at about the same time Galileo was first making his observations. However, since Marius did not publish his observations right away as Galileo had done, his claims were impossible to verify. Since Galileo's work was more reliable and extensive, he is generally given the credit for discovering the moons of Jupiter. In 1614, Marius did provide the names of the Jupiter's moons that we are familiar with today, based on a suggestion from Johannes Kepler:

"Jupiter is much blamed by the poets on account of his irregular loves. Three maidens are especially mentioned as having been clandestinely courted by Jupiter with success. Io, daughter of the River, Inachus, Callisto of Lycaon, Europa of Agenor. Then there was Ganymede, the handsome son of King Tros, whom Jupiter, having taken the form of an eagle, transported to heaven on his back, as poets fabulously tell . . . . I think, therefore, that I shall not have done amiss if the First is called by me Io, the Second Europa, the Third, on account of its majesty of light, Ganymede, the Fourth Callisto . . . ."

"This fancy, and the particular names given, were suggested to me by Kepler, Imperial Astronomer, when we met at Ratisbon fair in October 1613. So if, as a jest, and in memory of our friendship then begun, I hail him as joint father of these four stars, again I shall not be doing wrong."

The Galilean Moons (Galileo Images)
Ganymede, Callisto, Io and Europa

Galileo originally called the Jupiter's moons the "Medicean planets", after the Medici family and referred to the individual moons numerically as I, II, III and IV. Galileo's naming system would be used for a couple of centuries. It wouldn't be until the mid-1800's that the names of the Galilean moons, Io, Europa, Ganymede and Callisto, would be officially adopted, and only after it became very apparent that naming moons by number would be very confusing as new additional moons were being discovered.

From:  http://www.tau.ac.il/~museum/galileo/the_moons_of_jupiter.html
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