Yes, it should say Persian, not Iranian, for this period in history.
Actually the Iranians always called themselves Iranians and their country Iranshahr - right from Median times around 700 BC.
It is derived from “Aryan” i.e. the land of the Aryans. North Indians also called their land the land of the Aryans.
And note - “Aryan” means exclusively Indo-Iranians.
That’s why JRR Tolkien, when asked by a German if he was an Aryan wrote that “I have no Iranian, north Indian or gypsy ancestry, as far as I know”..
Germans aren’t “Aryans”, but a different branch of the Indo-European peoples. In fact the Poles, Russians and Ukrainians have more “Aryan” ancestry as the Scythi and Sarmatians roamed and at times ruled in those lands.