Answer
The full name is iron(III) chloride.
Work Step by Step
The charge on Fe must be 3+ for the compound to be charge-neutral with three Cl- anions. The name for $FeCl_{3}$ is the name of the cation, iron, followed by the charge of the cation in parentheses (III) and the base name of the anion, chlor, with the ending - ide. The full name is iron(III) chloride.