Her name is Madame Morrible in the musical. She is also the Secretary to the Wizard of Oz, but Elphaba and G(a)linda aren't aware of that till much later.
Madame Morrible.
A woman in charge of a school is typically referred to as a principal or headmistress.
Galinda but dr dilamond can't pronounce it so when he disappears she changes her name in his memory
Élfaba
headmistress
curancheple
Head
Nessarose.
Idena Menzel
Elphaba
Madam Morrible
Melena