In Halo 2, the former Covenant commander who becomes a playable character is given the title the Arbiter.
The Arbiter is a sacred military title in the Covenant. After failing to prevent the capture of Installation 04’s control room, the Sangheili commander Thel ‘Vadam is branded a heretic and nearly executed. Instead, the Covenant’s Hierarchs appoint him as the next Arbiter and use him for dangerous missions.
Players alternate between Master Chief and the Arbiter in Halo 2. The Arbiter’s missions reveal the Covenant’s internal politics and expose the conflict between the Sangheili and the Jiralhanae. His experiences eventually lead him to reject the Prophets’ manipulation.
The Arbiter is therefore both a title and the character’s commonly used identity. Thel ‘Vadam continues to hold the title in later games, but not every historical Arbiter is the same individual.