Learn Portuguese (Portugal): Como se chama a professora?

Yes, como literally means "how". The verb chamar means "to call", and se means "herself" (or "himself" / "yourself"). So, Como se chama a professora? literally translates to "How does the teacher call herself?". This is the standard Portuguese way to ask for someone's name.

The lesson says the pronoun usually comes after the verb with a hyphen, like "chama-se". Why is it "se chama" here?

That is a great catch! In European Portuguese, the pronoun usually goes after the verb as in chama-se. However, certain words act like magnets and "pull" the pronoun to the front of the verb. Question words like Como are magnet words, so they force the pronoun to come before the verb, and the hyphen is dropped.

Why is "a professora" at the very end of the sentence?

In Portuguese questions, it is very common to put the subject (a professora) after the verb. This is especially true when starting with a question word like Como. You could technically put it earlier, but putting the subject at the end sounds much more natural to native speakers.

If I wanted to ask about a male teacher, how would this sentence change?

You would only change the noun and its article to the masculine form: Como se chama o professor?. The verb and pronoun (Como se chama) stay exactly the same because the reflexive pronoun se is used for "himself", "herself", and formal "yourself".