Toge Inumaki is important too. His special cursed speech ability makes him stand out. Also, the principal of the school, Masamichi Yaga, is likely to be important as he is in a position of authority and has an influence on Gojo and the other students. There could be other characters like the members of different clans that also play roles in the complex web of the story.
I'm not sure as the term 'azure veil' could be something very specific in a fictional or made - up context. It might be a symbol, a name of a place, or an object within that particular story.
The black veil in the story is a symbol of mystery and sin. It sets the minister apart from the rest of the community and makes others wonder about his secrets.