Recall the naming rules for binary molecular compounds (compounds composed of two nonmetals): use prefixes to indicate the number of atoms of each element, and name the elements in order (first element name followed by the second element with an '-ide' suffix).
Determine the prefixes for the numbers of atoms: 'di-' for 2 nitrogen atoms and 'tri-' for 3 oxygen atoms.
Combine the prefixes with the element names: 'dinitrogen' for \(N_2\) and 'trioxide' for \(O_3\).
Put the parts together to form the full name: 'Dinitrogen trioxide'.