Not so new fact that many here may already know: The (in?)famous -stan suffix, coming originally from Persian, is an etymological cousin of State, Street, Statistics, Strategy and Stadt. In Iran, provinces are called Ostan and some Ostans' names end with -stan (e.g. Ostan of Kurdistan). By the way, since it's not clear from their names, it may be worth noting that Tajiki and Persian are two dialects of the same langu…
*Farsi. Persia doesn't exist anymore. I find it strange that somewhat uniquely people refer to Iran by its ancient name. We're not speaking anglo-saxonish
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.