Yes, that's quite a history. Especially if you consider that for a time ROC was permament member of security council of UN and after they were replaced by PRC, ROC was kicked out.
I think it should be fine though I don't know as I was never in east Asia. I will ask someone on TL who lives in Taiwan and get back here though I imagine simple "Taiwan" would be sufficient.
Update Apparently that would be very OK.
Thanks for being forthcoming :)
Ok, someone pointed out to me that these standard might be source of confusion.
If you look up here https://en.wikipedia.org/wiki/ISO3166-1#Namingandcodeconstruction in point two, Taiwan is not especially happy about this name. And as both mainland China and Taiwan China are heavily into esports, it might be better to just use "Republic of China (Taiwan)". For me that would just be fair to update the table this way.
So I stumbled into this subpage:
http://esportsearnings.com/countries
and it looks just plain weird. Taiwan is not "Province of China". It's independent country that mainland (PRC) China has no control over. So at the very least it should be just "Taiwan" and "China", though probably the most accurate would be to list them as i.e. China, Republic of and China, People's Republic of (for ROC and PRC, respectively).
Anyway - what's the deal with "Province of China"?