It was known as the “Persian Empire”
It only became “Iran” in 1935.
The people of Persia have been known as “Iranians”
since 1000 BC.
Interesting factoid:
“I am Darius, the great king, the king of kings
The king of many countries and many people
The king of this expansive land,
The son of Wishtaspa of Achaemenid,
Persian, the son of a Persian,
'Aryan', from the Aryan race”
From the Darius the Great's Inscription in Naqshe-e-Rostam"
Link: https://www.iranchamber.com/people/articles/aryan_people_origins.php