Eliot's joke carries more weight than it announces. The name everybody knows is the social mask — functional, necessary, the currency of ordinary life. The name that only a few know belongs to those close enough to have seen behind the mask: the intimate circle, the analyst, the friend who has watched you in crisis. Both of these names are still, in some sense, public property. They exist in relation to other people. But the third name — the one only the cat knows — belongs to no social contract at all. It is not withheld out of privacy or shame; it simply cannot be transferred, because it is not a label applied from outside but something more like the organizing core of what you are before the world began interpreting you.

Stein is pointing at what Jung called the archetypal layer of the ego — not the ego as social performer, not even the ego as private self-image, but the ego as rooted in something that precedes biography. Most of the work people call "knowing themselves" never reaches the third name. It stops at negotiating between the first two — adjusting the persona, managing the gap between public and intimate self. That negotiation is real work, but it is not the same as the encounter that Stein has in mind, which is less discovery than recognition of what was always already there.