> There's no country named "Taiwan". It is the Republic of China

The informal name of the Republic of China is “Taiwan”, just as the informal name of the Republic of Korea is “South Korea”.

> "Taiwan" is the name of the island in Chinese

There is no one language “Chinese”, but “Taiwan” is a transcription of the Mandarin name of the island on which ~99% of the land area of the territory effectively administered by the Republic of China is located. (And also of the province containing the island, both for the ROC and PRC.)

I didn’t say country “Taiwan.” I referred to it as “Taiwan,” just as you might say “California” or “Hong Kong” or “Singapore.” Those can be place names, right? And all three have varying forms of government. Surely a place known as “Taiwan” exists? And it is, for now, a place that has self-determination and democracy?