What is the correct name of #Fe_2O_3#?
There are both a correct modern (IUPAC) name and a correct historical name. Both distinguish between the iron oxidation states.
The IUPAC - International Union of Pure and Applied Chemistry - defines modern chemical nomenclature. Oxides are described with the metal atom first, followed by its oxidation state. Thus, the two forms of iron oxides are FeO and
The IUPAC designation for
The older historical names used the endings "ous" and "ic" to differentiate the two states. This is consistent with all oxide compounds (including "hypo", "hyper" prefixes for other values).
The former name for
In all cases, only calling it iron oxide is chemically incorrect.