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the media changed it to Farsi to reduce it's "prestige"This is not true.
It happened after the 1979 Iranian revolution, when Iranians abroad wanted to call it Farsi out of cultural pride, using the same word in their own language, rather than Persian which is the "foreign" word for it (from Greek/Latin). It was literally reclaiming the name. Then the media followed suit out of respect. It was cultural sensitivity.
Today some non-Iranians and therefore groups like the UN prefer "Persian" because variants are also spoken in Afghanistan and Tajikstan, and Farsi is a reference to the Fars province of Iran, so Persian can be seen as more neutral. But then again, not many people complain about "English" being associated with England and not being neutral enough to Americans or Indians. So it's definitely complicated. But it's also definitely not about trying to diminish anybody's "prestige".