Although the history of"Burma/Myanmar" is repeated with changing names, for them "Name is everything" and they strongly belive that "one's attitude follows one's name". There are instances where in people have changed their names for reasons such as this.
Many linguists feel that the name is spelled as "Myanmar", its actually pronounced as "Bhama". And this region is associated with the Land of Brahma ( One of the Gods in Hindu religion). This region was associated with Hinduism and Buddhism since ages. Slowly the land of Brahma got manipulated in to Burma... And the Britishers officialy made it as Burma.
As Usual, any nationalistic movement try to remove/address issues such as this. Hence the ruling government(which is actually a military ) changed its name to " Union of Myanmar" from the earlier "Union of Burma".