A well-educated woman who taught public speaking in Athens is called what

Aspasia

Explanation:

A popular woman, that was well-educated and moved freely in Athens and lived an unusual independent life. She taught public speaking to Athenians. She was love partner to Pericles. A very important Athenian in her own space. It was common site for female children to be seen not to be educated in Athens in those days. She is likely to be said to be the most famous and important entity of ancient Athens.