Yes it's Eldarion* but he also had 6 daughters with Arwen as well - there's not really much else to know about the kid. Tolkien kind of lost interest in it all for the Fourth Age after he killed off Sauron for the third time.
The immortality gig wore out with Arwen who died of grief and followed Aragorn into permanent peace outside the spheres of Arda (she didn't get to re-incarnate like proper Elves 'cos she chose to marry a mere mortal
) and their kids all lived happily ever after until they too kicked the bucket. All the Elves had sodded off into the West by then so nobody gave a damn....
*it means Son of the Elves apparently - both Arwen and Aragorn were descended from royal Elves - in fact she was his cousin several hundred times removed as he was descended from Elrond's twin brother Elros. Not a lot of people know that