Jellicle Cats have 3 names, the simple, real, and true names.

The simple name is the name given to them by people as a house cat.  Examples of such are.  Peter, Augustus, Alonzo, James, Victor, George, Bill Baily.  Fancier name might be Plato, Admetus, Electra, Demeter.

Real names are ones that the cat picks.  It is a ritual for when one comes of age, she must find a particular name fitted just so to her.  This is usually accomplished through a adventure ending in a ritual where the cat claims her name.  The name must be unique to her as no other living cat may be using it too.  If the name is already in use she will be cursed and have to go on a quest to cleans herself.  This is usually dangerous and so she takes care in the choice of her name.  Examples of Real names are Munkustrap, Quaxo, Coricopat, Bombalurina, or Jellylorum.

Finally a Cats tree name is very secret.  She is born with it and it is known to no other.  No normal human research can discover it, and she will never confess it].  If one know of it's True name she will be bound to there will till released, and at anytime reclaimed.    When you notice a cat in rapt contemplation, they are usually in deep meditation on the single ineffable, thought of their inscrutable name.