The name of the centaur who teaches Divination at Hogwarts is Firenze. He begins teaching the subject after Dolores Umbridge dismisses Sybill Trelawney during Harry’s fifth year.
Before joining the Hogwarts staff, Firenze lives with a herd of centaurs in the Forbidden Forest. Centaurs traditionally study the stars and interpret long-term cosmic patterns, while treating human-style fortune-telling with suspicion. Firenze’s lessons therefore present Divination from a distinctly centaur perspective, using planetary movements and celestial omens rather than relying mainly on crystal balls or tea leaves.
His decision to work at Hogwarts causes conflict with the other centaurs. They consider teaching humans a betrayal of centaur traditions and banish him from the herd. After Umbridge is removed, Trelawney returns to her post, but Firenze remains at Hogwarts and shares Divination teaching with her for a time.
A common mix-up is confusing Firenze with Ronan, Bane or Magorian. Those are other named centaurs associated with the Forbidden Forest, but Firenze is the one recruited by Albus Dumbledore as a Hogwarts teacher. The question’s wording identifies him specifically because he is both a centaur and a member of the teaching staff.