Because the job, for a number of reasons, can only be performed by a nine-lifed enchanter - the rarest and most powerful type of enchanter there is - the holders of the position tend be very special people. They also tend to spend a lot of time trying to locate a qualified successor.
Office-bearers mentioned or appearing in the series include:
The word Chrestomanci is a powerful charm that can be used to call Chrestomanci to the location of the caller. This happens in Charmed Life and Witch Week. This is a deliberately-left loophole so that people can call on him for assistance; he is otherwise carefully shielded against name-magic (for instance, there is a charm built into his signature to stop people using it against him).
Although this is not mentioned in any of the stories, the word "Chrestomanci" appears to be derived from the Greek word khrestos, meaning "useful".