[vanliyan]

Iranian Linguist here.

Persian is correct. If you want to go by what Iranians call it themselves when speaking English, you can even call it /'perʃijæn/.

If you want to call it as an educated Persian speaker, It's Parsi. "Farsi" is recent result of a lenition of starting /p/ in "Parsi", and is originally an informal way to say Parsi (starting in 13th century [Solar Hijri calendar]). For a source, if you go to https://ganjoor.net/ (A good source for all classical Persian poems) and search "فارسی" (Fârsi), the oldest Persian poem with this word you'll find is from 13th century [Solar Hijri calendar]. Literature teachers have recently started to address this in their teachings so the next generation will be calling the language Parsi again.

Both Persia and Iran are correct names (As said by son of the guy who renamed the country internationally). So Persia does still exist.