The Ministry of Foreign Affairs has a list of five names it can use when applying for membership of international organizations. They are pretty similar to each other and, with one exception, completely impractical.
First on the list, which is in no particular order, is the country's official title, the "Republic of China" (ROC). This name has become increasingly unpopular with ethnic Taiwanese, as it is the name of the Chinese Nationalist Party (KMT)-controlled government that settled here more than 50 years ago. Nevertheless, changing it would require amending the Constitution, which no one seems to want to do and risks a military response from China.
Internationally, it is confused with the People's Republic of China (PRC), as demonstrated by complaints about the nation's passport that prompted the government to add the word "Taiwan" in Roman script to the cover. Beijing's opposition to the term Republic of China means that the government can only use it in more obscure international organizations such as the Asian Productivity Organization, of which China is not a member.
Second on the list is "Taiwan." As the preferred name of independence supporters, it is completely unacceptable to China unless it is being used to represent a province of the PRC. Despite being the most recognizable abroad, perhaps thanks to the cheap plastic products churned out in the 1970s stamped with "Made in Taiwan," the name is divisive at home and impossible to use officially overseas.
Third is "Taiwan, Republic of China." It is odd that the Democratic Progressive Party government should find this name acceptable as it harkens back to the time when the government claimed all of China, of which Taiwan was only one part. It also suggests that Kinmen and Matsu are not included, because they are parts of the ROC that certainly aren't part of Taiwan.
Despite its inaccuracies, it contains the key word recognizable to foreigners: Taiwan. But the name written this way is probably now only found in addresses.
Fourth is "Republic of China (Taiwan)." This is the name that has been used in the past two bids to rejoin the UN. It is also the country's title in the Central American Bank for Economic Integration. It is little different from just saying Republic of China, apart from a suggested shorthand form has been tacked on the end in parentheses. Previous UN bids used Republic of China on Taiwan, even though the government had already given up any suggestion that it controlled the rest of China. Once again, it contains the key recognizable word but is unacceptable to China.
The last name on the list is "Taiwan, Penghu, Kinmen and Matsu." This name is the most acceptable to China, probably because it is such a mouthful that no one will be able to remember it, and it sounds nothing like the name of a country. When combined with a suitable prefix, such as "separate customs territory of" (the name used in the WTO), it becomes an unwieldy eight-word name. The acronym, SCTTPKM, doesn't really trip off the tongue either.
It is nevertheless being used to apply for observership of the World Health Organization (Health Entity of ?) and the Organization of Economic Cooperation and Development (Independent Customs Territory of ?).
But it does contain Taiwan, which almost certainly would be the shorthand version used by diplomats.