Chromium (III) chloride is correct.
All elements in the periodic table are represented by symbols, this is done to ease the representation of elements in chemical equation in writing. It is also done to differentiate one element from another.
Chromium is an element in group 6 (metals) of the periodic table. Chlorine on the other hand is an element in group 11 (halogen) of the periodic table.
The Roman numerals between the 2 elements indicate the oxidative state of chromium as many metallic elements have more than one oxidative state. Therefore the molecular name for CrCl3 is Chromium (III) chloride.
The periodic table is made of different elements. They are all arranged in order of increasing proton number such that there properties repeat after every 8 numbers. All of these elements have names, some big, some small. For ease, each element is also assigned a symbol to define it and make it easier to write.
Especially, these symbols were needed when balancing equations and molecules as it allowed the atoms to come to the front. CrCl3 consists of a metal chromium and a halogen called chlorine. Hence, its molecular name is Chromium (III) Chloride. The (III) defines the oxidation state of chromium in this molecule.