The point is that Taiwan claims to be the legitimate government of the whole of China (being the island where the former government fled to when the Communists took over the rest of the country - https://en.wikipedia.org/wiki/Chinese_Civil_War), and they express that by using "Republic of China" (as opposed to "People's Republic of China"). Similar to how there used to be a "Federal Republic of Germany" and a "German Democratic Republic". You could call both "Germany", but that would be confusing...
It is not confusing at all. Taiwan is a commonly used name for the ROC, and (mainland) China is generally understood as a reference to the PRC.
Since the de facto territories of the two states are common knowledge, you can unambiguously refer to them just by mentioning their rough position on the map. Similarly, East/West Germany were not officially called East/West Germany, and it was not the official name of either country, but people still understood what the words meant.
> The point is that Taiwan claims to be the legitimate government of the whole of China
Not since the early 90s.
Well actually it's a bit more complex since there are multiple parties and they disagree, and there's some nuance (e.g. "one China" but without actually defining what that means, exactly). But "Taiwan claims to be the legitimate government of the whole of China" is woefully outdated and incorrect.
That's mostly a symbolic legal fiction. And I'm guessing here but at least the half of the country who wants to be independent might prefer to be called Taiwan rather than RoC in casual conversation.
