That's the official name, of course, and primarily why there is an issue over UN membership for the country.
I know you mean no disrespect (in fact, you were probably giving a shout-out to Taiwan, so thanks), but tha lot of people in Taiwan who would take issue with the country being a "China." The country was under martial law for more than 30 years under the Nationalists and killed tens of thousands of people in the late 1940s. (I regret taking this thread off the topic of baseball.)
BTW, my friends in Taiwan would appreciate it if you support baseball in Taiwan!