The Capital City of Burma (officially named Union of Myanmar) is the city of Yangon.The population of Yangon in the year 2005 was 55,390,000. Burma is a Burmese speaking country on the coasts of the Indian Ocean and the Andman Sea.apital of Burma. The Capital City of Burma (officially named Union of Myanmar) is the city of Yangon. The population of Yangon in the year 2005 was 55,390,000.