The compound name for Mn₂S₃ is Manganese(III) sulfide. Here's how we arrive at that:

* Manganese: The metal is manganese (Mn).

* Sulfide: The nonmetal is sulfur (S), and its anion is sulfide (S²⁻).

* Roman Numeral: Since manganese can have multiple oxidation states, we use a Roman numeral to indicate its charge. In this compound, the manganese has a +3 charge to balance the -2 charge of the sulfide ions.

Therefore, the compound name is Manganese(III) sulfide.