That's a very interesting question. I've only ever heard it referred to as Farsi, so I didn't even know there was another option. Intriguingly, Wikipedia provides plenty of information, which seems to support your position (italics mine):
"Farsi, which is the Persian word for the Persian language, has also been used widely in English in recent decades, more often to refer to Iran's standard Persian. However, the name Persian is still more widely used. The Academy of Persian Language and Literature has maintained that the endonym Farsi is to be avoided in foreign languages, and that Persian is the appropriate designation of the language in English, as it has the longer tradition in western languages and better expresses the role of the language as a mark of cultural and national continuity. Iranian historian and linguist Ehsan Yarshater, founder of the Encyclopædia Iranica and Columbia University's Center for Iranian Studies, mentions the same concern in an academic journal on Iranology, rejecting the use of Farsi in foreign languages."
"Farsi, which is the Persian word for the Persian language, has also been used widely in English in recent decades, more often to refer to Iran's standard Persian. However, the name Persian is still more widely used. The Academy of Persian Language and Literature has maintained that the endonym Farsi is to be avoided in foreign languages, and that Persian is the appropriate designation of the language in English, as it has the longer tradition in western languages and better expresses the role of the language as a mark of cultural and national continuity. Iranian historian and linguist Ehsan Yarshater, founder of the Encyclopædia Iranica and Columbia University's Center for Iranian Studies, mentions the same concern in an academic journal on Iranology, rejecting the use of Farsi in foreign languages."
https://en.wikipedia.org/wiki/Persian_language#Name