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FIPS 10: Countries, Dependencies, Areas of Special Sovereignty, and Their Principal Administrative Divisions (FIPS 10) is maintained by the Office of Targeting and Transnational Issues, National Geospatial-Intelligence Agency, and published by the National Institute of Standards and Technology (Department of Commerce). FIPS 10 codes are intended for general use throughout the US Government, especially in activities associated with the mission of the Department of State and national defense programs.
STANAG 1059: Letter Codes for Geographical Entities (8th edition, 2004) is a Standardization Agreement (STANAG) established and maintained by the North Atlantic Treaty Organization (NATO/OTAN) for the purpose of providing a common set of geo-spatial identifiers for countries, territories, and possessions. The 8th edition established trigraph codes for each country based upon the ISO 3166-1 alpha-3 character sets. These codes are used throughout NATO.
Those list are correct to show Taiwan's name.
Taiwan, Province of China" has been made with pressure from the People's Republic of China over the political status of Taiwan.