And Burma is Bama, apparently. And Mama is the literary pronunciation of the more colloquial Bama. John Wells explains:
In Burmese, this name Myanmar is essentially just a variant of the name Burma. It is transliterated as Myan-ma or Mran-ma, and in the local language pronounced something like [ma(n) ma], as against [ba ma] for the traditional name.
According to Wikipedia,
within the Burmese language, Myanma is the written, literary name of the country, while Bama ... (from which “Burma” derives) is the oral, colloquial name. In spoken Burmese, the distinction is less clear than the English transliteration suggests.
So where did those R's come from? They're a British spelling convention to indicate long vowels:
What interests me now, however, is the question of how Americans and other rhotic speakers are supposed to pronounce this name. In both Myanmar and Burma the English spellings assume a non-rhotic variety of English, in which the letter r before a consonant or finally serves merely to indicate a long vowel: [ˈmjænmɑː, ˈbɜːmə]..
So any American who says the last syllable of Myanmar as [mɑːr] or pronounces Burma as [bɝːmə] is using a spelling pronunciation based on British, non-rhotic, spelling conventions.
I don't know anything about Burmese, and haven't checked the details involved here -- Bill Poser, who does know something about Burmese, may have more information to offer.
This reminds me that I'm still curious to know the truth about the "Burmese episode" at Yale that "was as funny to outsiders as it was painful for those involved". But there's certainly nothing funny about what's going on in Burma now (Seth Mydans, "A Few Voices From the Deepening Silence", NYT 10/14/2007):
Posted by Mark Liberman at October 15, 2007 07:17 AM
A young man described how the junta has clamped down on social exchange, destroying trust among people:
There is no more connection between people. It’s been broken. In our own neighborhood, the security groups will arrest anyone who is heard talking about these events. Even at tea shops we can’t talk about these things. These thugs will remember who you are and come to arrest you later. We can only talk to people we know on the street and never to strangers now. No one says anything at the market and everything has to be in secret. The bars have emptied out both because no one has any more money and what fun is it to get drunk when you can’t talk?
Even now we don’t dare take our transistor radios to listen to foreign broadcasts outside. Just in the last few days, we have been threatened with arrest by local authorities for doing this in our ward. Anyone with a cellphone or camera will have it confiscated.