What is the correct name for N^3-?

The correct name for N^3- is a) nitride ion.

Explanation: In chemistry, the charge of the nitrogen ion is important for determining its name. The nitride ion specifically refers to nitrogen when it has a -3 charge (N^3-). Other options like ‘nitrogen ion’ (b) and ‘nitrogen III ion’ (c) do not accurately describe the -3 oxidation state. ‘Nitro III ion’ (d) is incorrect as it refers to a different type of nitrogen compound, and ‘nitrite’ (e) refers to a nitrogen compound with a +3 oxidation state. Therefore, the name that accurately represents N^3- is the nitride ion.