The characters for Yagokoro literally mean "Countless thoughts", i.e. "Boundless wisdom" (the number eight in names means "infinite/countless"), and Eirin "Eternal jewel".
A genius pharmacist who once lived on the moon. Kaguya persuaded her to produce the forbidden Hourai Elixir—the elixir of life—and consumed it. They were found out, and Kaguya alone was punished and was sent to the Earth, a fact which Eirin always felt guilty about. Sometime later, the moon court pardoned Kaguya's sins and summoned her back. Eirin and a handful of emissaries were sent to retrieve her, but Eirin found out that Kaguya didn't want to return to the moon. Acting out of her past guilt, Eirin betrayed and murdered all the other emissaries under the eyes of the earthlings who had fostered Kaguya. Eirin bribed the earthlings with the Hourai Elixir, in order to keep them silent, and went into hiding with Kaguya in Gensokyo.