Did the wicked witches of Wizard Oz have names?

The wicked witch in The Wizard of Oz has one name, the Wicked Witch of the West, also known as Elphaba in the musical Wicked and as Mombi in some early drafts of the novel The Wonderful Wizard of Oz. There is no mention of other wicked witches in either the novel or the 1939 MGM film.