One who habitually practices illeism, that is, refers to oneself in the third person. Favourite locution of royalty and pedantic professors.
This five dollar word is rather obscure; it's not in many of my usual dictionary sources. The strangest thing is that when I enter it into Google I get nine sites (maybe ten after I post this), and they include "Adults only -- Nice Big Asses paradise!" and "HOT German Breast Bondage Shows!!" Maybe illeist has an illicit meaning in some other language that would lead pron sellers to put it in their keywords, but in English this just doesn't make sense.