Why Did Burma Change Its Name To Myanmar, And Which Name Should We Use Now?

In the native ("Burmese") language, Myanmar is the name of the country previously called (in English, by most everyone) Burma, or the Union of Burma.  The name Burma comes from the ruling elite and population majority in the country, who were traditionally the Bamar, or Burmans (Burmanese).  The people of Burma/Myanmar might better be referred to as the Myanma people, which name would refer to all ethnic groups living there.

In 1988 a military junta seized power in Burma, changing the name to Myanmar in 1989.  The renaming probably would have passed off without comment except for the illegal and violent way the junta had seized power; many outsiders see this government as having no right to rule, and certianly not to change the country's name.  What's worse, the junta disregarded the results of national elections in 1990, which should have The National League for Democracy to power, effectively imprisoning the party leader, Aung San Suu Kyi instead for the last 18 years.

So at the moment, the country's name is in limbo, from an international perspective.  Myanmar may actually be a better (more representative name for the people living there) of the country, but using the new name may be lending legitimacy to a brutal regime that does not deserve to be in power.

I think, Myanmar is what people call it now but, many people still refer to it as "Burma"

The problem of which to use is definitely political- calling it "Burma" says you don't agree with the legitimacy of the current government, since they changed the name as part of trying to be a supposedly "people's" movement in opposition to the old ruling elite from colonial days, when really they're no more legitimate. Calling it Myanmar tacitly endorses the situation, or at least accepts it as it is. And of course, for conversation in English, Burma is much easier to say than Myanmar, so speaking informally we tend to use the old name.