Identify the elements present in the compound N2O3: nitrogen (N) and oxygen (O).
Determine the number of atoms of each element in the compound: 2 nitrogen atoms and 3 oxygen atoms.
Recall the naming convention for molecular (covalent) compounds: use prefixes to indicate the number of atoms (mono-, di-, tri-, tetra-, penta-, etc.).
Apply the prefixes to the elements: 'di-' for 2 nitrogen atoms and 'tri-' for 3 oxygen atoms, resulting in 'dinitrogen trioxide'.
Confirm that the first element keeps its full name and the second element uses the '-ide' suffix, so the correct name is 'dinitrogen trioxide'.