Illeism is the habit of referring to oneself in the third person. Strictly speaking it refers to excessive use of the pronoun he, because it derives from ille, its Latin equivalent. That’s why it’s said like illy-ism.
It is most often found in books about Shakespeare’s plays, in particular Julius Caesar, in which characters often refer to themselves in the third person, a trick that Shakespeare took from Caesar’s own writings. Characters in fiction sometimes refer to themselves in the third person, which can be an authorial device for indicating idiocy or overweening self-importance. Neither applies to Salman Rushdie’s new book, a record of the years he spent in hiding from the risk of retaliation by Muslims against The Satanic Verses. His book’s title is Joseph Anton, the pseudonym Rushdie took during this period; he distances himself from his alter ego by using the third person.
Illeism was coined by Samuel Taylor Coleridge in 1809 as the inverse of egotism, a mark of which is overuse of the pronoun I. Coleridge also invented tuism, meaning to refer to oneself as thou (on occasion people then still used thou as a familiar second-person pronoun equivalent to French tu, from which he took the name). Tuism also means giving priority to the interests of other people rather than oneself:
The professional’s attitude is or ought to be one of “tuism” — in other words, he is concerned, through beneficence coupled with integrity, to promote the interests of his clients.
Ethics in Education, by David Fenner, 1999.
The plural equivalent of illeism is nosism (from Latin nos, we), referring to oneself as we, It’s often called the royal we, though it’s not much heard even from royalty these days (“We are not amused”). It can also be the editorial we, since commentators like to use it in the hope that they will sound like spokespeople for the public, or at least the organisation for which they write.