…Myanmar (Burma...I'm unclear on the proper nomenclature here as Myanmar is the official name, but last time the country was in American news, articles were pointing out that that was a military coup imposition and Burma was better...I should add "what do I call this country" to my question

The official name of the country in English is Republic of the Union of Myanmar, or just Myanmar. But that's just the official English name and doesn't in any way reflect a change in the name of the country as it's called in Burmese.

In fact just to show how much of a non-issue it is for people speaking Burmese, the -ma in "Burma" and the -mar in "Myanmar" are the same exact thing in Burmese. မြန်မာ is how you write "Myanmar" /mjə.mà/, and ဗမာ is "Burma" /bə.mà/. The latter is just a more colloquial/informal version of the name. You'll notice that in the Burmese script the last part is <မာ> in both cases.

In other words, in Burmese, both names are used, and while for official use by foreign heads of states, it might show some position one way or the other toward the ruling government, in actual speech it's not like one's wrong and the other's right. They're both right. They're just different speech registers.

It's similar to the issue where the Iranian government says we should call the language Persian instead of Farsi but plenty of people still call it Farsi and it's not something that really causes offence, but actually it's even more neutral than that, since both names are used in spoken Burmese all the time, unlike "Persian". Point is, Burma isn't a derogatory term.

For what it's worth, the trend of only ever saying "Burma" if you don't like the government is changing, and for the most part — at least in recent news broadcasts of heads of state — people seem to be more or less over it as a form of protest. I imagine in a few years time the only people having an opinion on the matter will be people who don't actually have any personal/academic connection to the country.

This is old, but in Southeast Asia, long before the arrival of European Colonialists, there was low-land/high-land conflict. The lowland viewed itself as representative of "civilization", which literate cities supported by wet rice agriculture. The highlands were very often out of the control of the lowland states, and to have a "tribal" organization (that is, somewhat overlapping political units based on, perhaps fictive, kinship and descent) and to have more varied food sources, often using root crops and swidden (slash and burn) agriculture rather than wet rice patties.

Much of Burma is an area sometimes called "Zomia", a term coined by a Dutch geographer in 2002 and popularized by a hero of mine, James C. Scott, in his excellent monograph 2009 The Art of Not Being Governed. These sorts of highland/lowland conflicts have been going on roughly since states emerged in the lowlands, though they have taken many, many forms over the years. Today, paved roads, all terrain vehicles, and helicopters have given the lowland states power in the highlands that they never had before and many of these highland groups that have been traditionally outside of the state system (or who have been part of an alternative state system) have been fully brought into the state.

You may have heard of the Hmong from China, Vietnam, and Laos, as they're one of the most famous upland groups because of their involvement in the Vietnam War (which helps explain the large Hmong diaspora in the U.S.), but they're one of dozens of upland groups in the region. The Shan and Karen groups of Burma, Laos, etc. might be the second and third most famous groups. Burma/Myanmar is an interesting case in the region because they're the one with by far the largest population of minority groups. Vietnam is 86% Kinh/Viet, Thailand is 90-95% ethnic Thai (confusingly including Thai Overseas Chinese), Cambodia is about 90% Khmer. Laos is roughly 60% Lao, and Myanmar is roughly 68% Bamar. I know less about Laos than any of the other countries (and I don't know much about any of them), but I think in Laos you have minorities that are much more part of the state system (i.e. practicing terraced wet rice agriculture) than in Burma. Now, social science research has demonstrated that mere presence of ethnolinguistic heterogeneity does not actually increase a country's change of ethnic civil war, ceteris paribus; however, the uneven distribution of power across ethnic groups does. For instance, we see little ethnic conflict between Azeris and Persians in Iran because both are very deeply enmeshed in the Iranian state. Across the border in Turkey, we see a lot of conflict between the Kurds and Turks as Kurds feel they are systematically excluded from the state system. Anyway, I know little about the specific relations of pre-colonial Burma, but I can imagine it was similar to that of neighboring states and their conflicts with their own "hill tribes".

However, that is not say that the entrance of bureaucratic states, nationalism, and changing economic relations couldn't have exacerbated pre-existing conflicts and frozen cleavages that were once more malleable. But I thought you might be interested in a little more context. If you have an hour to spare, I strongly recommend listening to this lecture by James C. Scott which summarizes his book (it's a video, but I don't remember the pictures are particularly useful or important so you can listen to it like a podcast). His book does have some critics (often loving critics) who seek to complicate his model, but it has already been quite influential in history, anthropology, and political science and seems to form sort of a good "baseline" for what's going on. My friends who study upland regions of the Ottoman and Persian Empires in the 19th century were so excited about the book because they feel that many, many of the features easily translate from Southeast Asia to the Middle East, and apply not just to mountains but to marshes and deserts (i.e. the Marsh Arabs in Iraq, the Bedouins in Arabia and North African deserts)--something that Scott himself suggests in his book, but doesn't explore very much because it's largely outside of his scope.

The point is, I suppose, that Burma itself was a form of empire, in that a single state was formed by one ethnic group which dominated the others, forming what was described as the "Kingdom of Burma" in late 18th century British sources, for example. That one ethnic group was dominant would tend towards the other ethnic groups seeking some sort of autonomy or independence whenever the ruling group appeared to be weak, hence the Kerens and the Shan opposing the government. As for the British "stomping in", it is possible that Britain might have got involved in Burma anyway, at some point, but Britain's military involvement in Burma began when the Burmese invaded British (HEIC) India in 1824. Burma had been aggressively expanding its territory, and subjugating its neighbours, for some time, until her borders became common with British territory. Essentially, it was a clash of two empires, which the stronger empire won.