"Persian" is a historical mistake started by Herodotus, Iran was Iran from the begining. start to learn the proper name after a long time 2500+ years is a long time.
You are correct that Iran has always been called Iran (Eraan).
Persians refer to the sub-set of Aryanman of Eran-Zameen ["Land of Arya"] that settled in the general area of the province of Fars (Perse) and after the overthrow of the Median Aryanman (likely forefathers of the Kurds) ascended the world stage [1].