What is the name of Hel's hall in the underworld?

The name of Hel’s hall in the underworld is Eljudnir.

Eljudnir is an Anglicized spelling of the Old Norse Éljúðnir, the hall belonging to Hel. In Snorri Sturluson’s Prose Edda, Hel rules over the realm of the dead and resides in Niflheim, where this hall is located. The name is often translated with imagery such as “sprayed with snowstorms” or “damp with sleet or rain.”

The hall’s details are unusually grim. Its entrance threshold is called Fallandaforað, “falling to peril.” Hel’s bed is named Kör, meaning “sick bed,” and its bed curtains are Blikjandaböl, a name translated as “Gleaming Disaster.” These descriptions reinforce the hall’s association with illness, cold, and fatality.

Eljudnir is mentioned in only a limited portion of the surviving mythological record. It should not be confused with Valhalla, Odin’s hall for many warriors slain in battle, or Fólkvangr, Freyja’s field. Nor is it Sessrúmnir, a hall associated with Freyja.