Guys, we’ve been over this. You shouldn’t call the language Minnan, as that’s the name of the linguistic sub-family-group invented by a linguist, 趙元任, in the 1930s, so saying there is a language named Minnan is as idiotic as saying there’s a language named Romance. Imagine someone saying “I speak French”, and some dude insists “no, you speak Romance, French should be the language spoken by the Franks near Frankfurt.”
Taigi speakers didn’t choose to name their language Taigi. It’s yet another exonym that dates back at least 200 years. Taigi aka Taiuanue has been called that by officials since the Qing dynasty. It was called that by the Japanese. It was called that by the KMT. CKS even sponsored a dictionary using Zhuyin to spell out Taigi, titled “Zhuyin for Taigi Phrases”.

Saying Taigi shouldn’t be called Taigi because there are other languages in Taiwan is as silly as saying Hakka shouldn’t be called Hakka because Hakka means immigrants, and there are other immigrant languages in Taiwan, one of which is Taigi.
Let’s rehash a rehash. The current form of Mandarin did not come into existence until the late 1800s.