Politically correct term use to identify the country
Taiwan, as approved by the government of the People's Republic of
China. It may be used in international events like sporting fixtures or conferences.
The official name "Republic of China" is verboten because to Beijing it legitimises the government on the island (which to date considers itself the lawful government of all of China right up to Kazakhstan). And the name "Taiwan" somehow is also disliked, perhaps because the name of the island synonymously eludes to independence.
So instead Chinese Taipei is used, with the name of the largest city following the adjectival form of China. Conveniently Beijing can think that the adjective suggests possession, while the Taiwanese government would say that it merely describes China's cultural legacy on the island.
In an era of nation-states, where modern countries are not supposed to define themselves by any one ethnic group that resides within (at least not too obviously), the Taiwan question is a bit of an anachronism. Except that both countries are armed to the teeth and seem ready wage over how it defines itself on the back of a competing athlete's tracksuit.
The country is described using the capital city because Taipei is not a town in China (and neither is Tipping...ha de har har).