What is the name of the heavenly rock cave where Amaterasu hid?

The heavenly rock cave where Amaterasu hid is Ama-no-Iwato.

According to the Kojiki and Nihon Shoki, Amaterasu retreated into Ama-no-Iwato after her brother Susanoo’s destructive and insulting behavior. When the sun goddess sealed herself inside, the world was plunged into darkness, and the other kami had to devise a way to bring her back.

The gods gathered outside the cave and staged a noisy celebration. Ame-no-Uzume performed a comic, provocative dance, causing the assembled deities to laugh. Curious about the commotion, Amaterasu opened the cave slightly. She saw her reflection in Yata no Kagami, and Ame-no-Tajikarao pulled the door open so light could return to the world.

Ama-no-Iwato is sometimes confused with Takamagahara, the heavenly realm where many kami reside, or Yomi, the underworld associated with the dead. The cave is also linked with Amanoiwato Shrine in Takachiho, Miyazaki Prefecture, where the sacred site is worshipped.