The correct name for the compound CoCl₃ is cobalt(III) chloride. Here's why:

* Cobalt (Co) is a transition metal that can have multiple oxidation states.

* Chlorine (Cl) has a -1 charge in its ionic form.

* To balance the charges, cobalt must have a +3 oxidation state.

* The Roman numeral III in parentheses after "cobalt" indicates the +3 oxidation state.

Therefore, the full name of the compound is cobalt(III) chloride.