This is an unmarked miscellaneous quest. The title "The Name" will not appear in game anywhere.
After the player completes the final Hero Path, the Guide Spirit will prompt the player again to speak about something.
Asking the Guide Spirit, “You wanted to talk about something?” will prompt her to explain that she remembers an item that was precious to her and where she lost it. The player can offer to try and find it for her, and if so is prompted to head to the Sightless Pit.
When approaching the pit, the Guide Spirit will make a comment, and again when near the entrance, and once more once inside.
The item in question is a unique doll item found in the boss chest of the location. When the player picks it up, the Guide Spirit will attempt to forcegreet the player. If they cannot for whatever reason, then speaking to her will kick off the following dialogue regardless.
She will request to be given the doll. If the player declines, the quest fails. If they do give it to her however, she finds a ring on it inscribed with her real name: Eir. From this point onward, the Guide Spirit will be named “Eir” when not posing as one of the other follower spirits. She will also give the player the ring Whisper of the Departed - which allows the player to move silently - as a reward, and the quest completes.