Of course, we don’t have an Academy in English to adjudicate on these matters, but we do have precedent and practice. Persian remains much more common, but there is some usage of Farsi. Wikipedia (Persian language) says:
The Academy of Persian Language and Literature has declared that the name “Persian” is more appropriate, 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. Some Persian language scholars such as Ehsan Yarshater, editor of Encyclopædia Iranica, and University of Arizona professor Kamran Talattof, have also rejected the usage of “Farsi” in their articles.
What Persian scholars like, I have to say, is not particularly decisive about how English will work, although English favours endonyms much more these days than other languages do. Or rather, a bunch of English-speakers do; I don’t, harrumph.
Both are used, use Persian as the default unless you have reason not to.