What is the name of the compound with the chemical formula #CrCl_3#?
The most important thing to realize here is that you're dealing with an ionic compound that has a transition metal as its cation.
This should automatically tell you that the name of this ionic compound must contain a Roman numeral.
As you know, transition metals can have multiple oxidation states. Roman numerals are used to distinguish between these possible oxidation states for the transition metal cations.
Now, your anion, which is the negatively charged ion, will be the chloride anion,
Since the formula unit contains
This means that the chromium action will be in its
So, the cation is
The name of this ionic compound will thus be
As a fun fact, anhydrous chromium(III) chloride is violet in color.
Here is a video with some more examples of this concept.