Natalie, the names "China," "Republic of China" and "Taiwan" are not interchangeable and have different meanings "Republic of China" is not an "official name for Taiwan"; the categories must be structured and named in a correct and nonanachronistic fashion.
If I can draw an analogy, it's like "The Holy See," "Vatican City", "Rome", and "The Catholic Church" are not equivalent. You would not call Francis the "Pope of the Vatican" although that is the geographic seat of the Holy See, part of its sovereign territory and where he governs from; "Category: Vatican, Popes" would be wrong.
The history of China, Taiwan, and the Republic of China are complicated and controversial. For decades following the Xinhai Revolution, the Republic of China was a mainland Chinese state; it contended with the Beiyang government and Japan/Manchukuo, and was then relegated to Taiwan following the CCP's ascendancy in the Chinese Civil War.
As recently as 2008, President Ma Ying-jeou reasserted the Republic of China's sovereignty over all of mainland China.
Chiang Kai-shek led the KMT government of the ROC from Mainland China including his initial term as president of the ROC under its fifth constitution before retreating to Taiwan in 1950.
It is the Republic of China that has a president. This is further complicated by the fact that there is a push for "Taiwanification" by the DPP and similar parties however even in DPP official publications the office of President is referred to as of "Republic of China" or "Republic of China (Taiwan)". Taiwan is an island; it is also widely used to refer to a nation (notwithstanding its lack of diplomatic recognition) which includes various other small islands (like Penghu, Kinmen, Matsu, Lanyu etc). But there is a distinction between Taiwan and the Republic of China which is all the more important given its peculiar status. It is not strictly correct to refer to the "President of Taiwan" although this may be widely understood.
I hate to appeal to google but "President of the Republic of China" has 3.7 million hits to "President of Taiwan" having 1 million, despite it being wordier and more obtuse to English-speakers not familiar with the Taiwan situation; also Wikipedia's page is "President of the Republic of China", even though "Republic of China" is a redirect to "Taiwan."
Also to your earlier point, I wasn't arguing that English shouldn't be used for the category names, rather for the proper English name, but on that note, while "Taiwanese Hokkien" is the majority mother tongue in Taiwan, until a year ago the only official language of the Republic of China was Mandarin (the current administration additionally recognized Hokkien ("Taiwanese"), Hakka, and the aboriginal Austronesian languages in 2019). But the government in English publications refers to the President as President of the Republic of China.