The sprite for the man she is talking to is a placeholder since he's not designed yet (and I wanted to write this scene). His name is Dilan, and he's a critical character to the story-- basically when Garden resumed being a school, Cid hand-picked a new Headmaster to oversee school-based shenanigans and be a higher authority. He's a bit of an enigma, but in this scene you see he puts a lot of thought into his students, his decisions, and Garden itself, so the party (including Squall) have quite a bit of respect for him.