Final answer:
The correct name for the compound Li2CO3 is dilithium carbonate, following the conventional rules for naming ionic compounds.
Step-by-step explanation:
The correct name for the compound with the formula Li2CO3 used in the treatment of manic depression is dilithium carbonate. In naming ionic compounds, the cation (positively charged ion) is named first followed by the anion (negatively charged ion). Since lithium (Li) has only one common oxidation state (+1), there is no need to indicate its charge in the name. Additionally, the compound contains the carbonate anion (CO32-), thus the name of the compound is straightforwardly dilithium carbonate.
The other options provided are not correct because they do not adhere to the conventional naming rules for ionic compounds.