Recall the naming conventions for binary molecular compounds composed of two nonmetals, which use prefixes to indicate the number of atoms of each element.
Determine the prefix for the number of nitrogen atoms: 'di-' for 2 nitrogens, and for oxygen, since there is only 1 atom, the prefix 'mono-' is used but often the 'o' is dropped for ease of pronunciation.
Combine the prefixes with the element names: 'dinitrogen' for \(N_2\) and 'monoxide' for \(O\) (oxygen with one atom).
Thus, the correct systematic name for \(N_2O\) is 'dinitrogen monoxide'.