> 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.)
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.)