A country with two names, both seemingly correct, but it all depends on who you are talking to. The same applies to the largest city, which also goes by two names, Rangoon/Yangon.
The name Burma has been used in some variety since the 18th century colonial period, and both Burma and Myanmar are an ethnonym of the majority Burmese population. In 1989, the Military Junta government officially changed the name to Myanmar, but recognition of this internationally and even within the country is sporadic.
Opposition parties in the country, and opposition leaders such as Aung San Suu Kyi still refer to the country as Burma, as do most western nations. The United States still refers to the mission as U.S. Mission to Burma or U.S. Embassy Rangoon.
When it comes to filing out visas or government paperwork however, you better spell it Myanmar, or your application is likely to be rejected.
Ultimately it seems to boil down to how passionately pro military government someone is about the country but saying either doesn’t seem to ruffle too many feathers of the average person.