Here's how we arrive at that name:

* Cobalt: The metal in the compound is cobalt (Co).

* Oxide: The nonmetal is oxygen (O), which forms the oxide ion (O²⁻).

* Roman Numeral: Since cobalt can form multiple ions, we need to use a Roman numeral to indicate its charge. In Co₂O₃, the cobalt ion has a +3 charge (Co³⁺) to balance the three -2 charges from the oxide ions.

Therefore, the name is cobalt(III) oxide.