Final answer:
The specific Greek name for the "unspeakable things" during the Eleusinian Mysteries is not clearly documented, but the general term for the rites is 'mysterion', implying secrecy surrounding the experiences of the initiates.
Step-by-step explanation:
The Greek name given to the "unspeakable things" that happened during the Eleusinian Mysteries, particularly in the highest degree of initiation known as the epopteia, is not explicitly mentioned in the historical sources. The Eleusinian Mysteries were highly secretive religious rites, and details of what occurred during the ceremonies were closely guarded by initiates. It is speculated that during the epopteia, initiates were shown sacred objects and participated in dramatic reenactments of the Demeter and Persephone myth. Mystery in ancient Greek is mysterion, a term associated with the verb myein, meaning 'to close the eyes or lips', and this implies a necessity for secrecy about what was experienced or seen during these rituals.