Here's why:

* Copper (Cu) can have multiple oxidation states, so we need to specify which one is present in the compound.

* Iodine (I) has a charge of -1.

* CuI₂ indicates that two iodide ions (I⁻) are needed to balance the +2 charge of the copper ion (Cu²⁺).

Therefore, the correct name is Copper(II) iodide.