That is in dispute and depends on which party is in power, by the year. Until general elections were opened up in the late 80s, it was definitely the Republic of China.
The Democratic Progressive Party led coalition would change the name on the passport the government issues when it is in power. It would revert back when the Koumingtang led coalition comes back into power. It falls in line with what the constituents want, and it isn't as if opinions of the citizens are uniform or a clear majority.
The situation is fairly complex.
Since this is intended as a historical map going beyond the Bronze Age, there weren't always a thing called a constitution or international law. So while this does apply to whether we call this polity, "Taiwan, ROC" or "ROC" or "Taiwan", whether something is constitutional or not will not always apply historically.
