What is the name of #N_2O_3#?
It is Dinitrogen trioxide.
The name of the oxides is made by putting the name of the other element first with its number(mono if its 1, di if its 2, tri if its 3, ...) and then the oxide with its number.
So, in this case we have two atoms of nitrogen - Dinitrogen - and three atoms of oxygen - trioxide.
Putting them together: