as far as i searched Japanese people have informal relations with Taiwan and is close to them in someway but i couldnt find a proper politically correct official name for them other than finding out it used to be formally called フォルモサ some decades ago. is it just plain Taiwan 台湾/たいわん always then just like Japan is both officially Japan and short name is Japan too?
According to this article, the Japanese government officially calls Taiwan 中華民国 (Republic of China) for diplomatic reasons, and pretty much every other organization, the media, and individuals use 台湾 (Taiwan).