The Jewel was never mentioned by any name except for "The Jewel."
The Desert Oasis Jewel's existence was revealed to Jack when he looked deep into the Light of Eternity. It was revealed to Jack that the Jewel had great magic abilities. While it was not specified what kind of magic abilities the jewel possessed, the fortune teller who was the purveyor of the Light of Eternity assured Jack that it possessed the ability which he was looking for: time travel. Though the fortune teller warned Jack that only someone who was pure of heart could use the power of the jewel.
Jack traveled through the desert with Ikra (Aku in disguise) and found the jewel. It was a large green gem that floated above a small pool of water which was made green by the light of the gem. The Jewel tested Ikra and Jack, found that Ikra was evil, and was not pure of heart, and revealed the guardian of the jewel to be a large blue beast which fought fiercely, but lost to Ikra. The Jewel was placed on the forehead of the guardian. When the guardian lost, Aku smashed the jewel on the ground and revealed that he had only came along to ensure Jack's failure.
It was likely that the jewel was restored after Jack had destroyed Aku in the past.