Regardless of them getting explicitely identified to the wards, so it must get its names independently.

If it must, then Dumbledore overrode it.

He did so specifically to prevent himself from learning the Defense Professor's identity, because that was the term stipulated by Quirrell.

Those lines were specifically included to keep the story from prematurely reaching its climax as soon as Quirrell returns to Hogwarts. I think you will enjoy stories more if you accept that sometimes things happen for story reasons.