The compound CrO$_3$ is known as Chromium (VI) oxide, or chromic acid anhydride. It contains chromium in the +6 oxidation state, which makes it a strong oxidizing agent. Chromium (VI) compounds, including CrO$_3$, are highly toxic and are used in various industrial processes such as metal finishing, tanning, and as a catalyst.
Chromium (III) oxide is Cr$_2$O$_3$ and contains chromium in the +3 oxidation state.
Chromium (IV) oxide is CrO$_2$ and contains chromium in the +4 oxidation state.
Chromium (V) oxide is less common and is represented by Cr$_2$O$_5$, containing chromium in the +5 oxidation state.
Thus, the correct name for CrO$_3$ is Chromium (VI) oxide.