So the best I could find is Jove is an anglicized alternative to Jupiter, deriving from the declension of 'Juppiter' in Latin: Juppiter (nominative), Juppiter (vocative), Jovem (accusative), Jovis (genitive), etc. 'Jove' tends to be slightly more old-fashioned in English translations, but rest assured it's the same jolly deity.  I never understood why Richard is called sometimes Dick, or John can be called Jack.  Now when it comes to Ulysses vs Odysseus, the Roman name vs the Greek name, that makes sense.