What was the real name of the witch from 'The Wizard of Oz'?

In the book The Wonderful Wizard of Oz:

Glinda is the Witch of the South. The other witches are only known as "The Wicked Witch of the West," "The Wicked Witch of the East," and "The Good Witch of the North."

In the movie The Wizard of Oz:

Glinda is the Witch of the North. The other witches are only known as "The Wicked Witch of the West" and "The Wicked Witch of the East."

In the book Wicked:

Galinda, later Glinda, is the Witch of the South,

Elphaba is the Witch of the West,

Nessarose is the Witch of the East,

and the Witch of the North is never mentioned or named.