The name of the paradise for heroes in the underworld is Elysium.
In Greek mythology, Elysium—also called the Elysian Fields—was a blessed afterlife reserved at first for heroes, demigods, and mortals with special connections to the gods. Unlike Tartarus, a place of punishment, Elysium offered peace, happiness, and an existence free from ordinary suffering.
The idea changed over time. In Homer’s Odyssey, Elysium lies at the western edge of the world near Oceanus, and entry is limited to favored figures. Later traditions broadened admission to include the righteous and those chosen by the gods. Hesiod associated a similar destination with the Isles of the Blessed, while Pindar described a pleasant realm of parks, music, and athletic pursuits.
Elysium is often confused with Olympus, which is the home of the gods, not the normal destination of heroic human souls. Asphodel is a more ordinary region of the underworld, while Tartarus is associated with severe punishment. The Roman poet Virgil later gave Elysium a prominent role in the Aeneid.