I know that the Arbiter wasn't originally planned to be called the Arbiter and that the developers had other names planned for him.
What were those names and why was it eventually decided to use "Arbiter"?
The Arbiter was originally meant to be called the "Dervish". The name was changed because it might create an unintended parallel between the game and the real-life conflict between the Western World and the Middle East.
In the Spanish version of Halo 2 and Halo 3, the Arbiter is called "Inquisidor". This is because the false cognate "árbitro" means "umpire" instead of "Arbiter".
The Arbiter's original name is Thel 'Vadam, Arbiter is a title/role given by the Prophets and typically sent on suicidal missions for the covenant to die and become a "martyr" for the Great Journey.