"The name "Vietnam" has been official since 1945. It was adopted in June by Bảo Đại's imperial government in Huế, and in September by Ho's rival communist government in Hanoi." source
Additionally, the U.S. State Department used "Vietnam", "Viet Nam" and "Viet-Nam" for the same nation, with an internal preference for "Viet-Nam" in the 1960s. Oxford dictionary list all three formats as acceptable spelling for the nation. The single word name fell out of use in the early 1980s with several historians noting the hyphenated spelling was dated.
In the United States, referring to it as "Viet Nam" is generally seen as a sort of offensive following the Vietnam war and the pronunciation of the word so that the second syllable rhymes with the word "Scam" is seen as something said by people with slight prejudicial views (I believe it was used by Military and Government officials as it was period correct pronunciation. It can be heard prominently pronounced this way in the movie Forest Gump). Today it is more commonly pronounced so that the second syllable rhymes with the first syllable of "Nominate". I am unaware of the actual offense taken by the country or the people at either pronunciation.
In short, while all three spellings are correct, in most English speaking countries, Vietnam is preferred, though the "Viet Nam" spelling is used by the UN and the Vietnam government itself.
Most countries do not have the same name or direct translations in non-native languages. For example, the United States' official Chinese Name is translated as "The Beautiful Country" (the word Mei is the Chinese word for Beauty and sounds like the Second Syllable in "America"). Historically, China referred to the nation as "The Country with the Patterned Flag" due to the unusual design of the U.S. Flag on ships in the ports of China. While this is quite dated to a modern Chinese speaker, it's still used by several American entities that were in China when it was in vogue (Predominantly Citibank of America's Chinese name uses the old name for the United States). Neither would be particularly offensive to the average U.S. Citizen who doesn't have a good grasp of the Chinese Language and both are still positive stereotypes of the U.S. they hold about themselves.
Unless a particular name is very offensive, most nations do not mind their names from other cultures and do not protest often. Most renamings stem from poor transliliterations of the sounds used in the original language to the new language (ala Peking is a Romanticized name for Beijing based on a Southern dialect) or confusion (Mumbai was historically called Bombay after the Portuguese, which referred to the city's bay as Bom Bai or "Good Bay" before the British came to India. Either way, the citizens saw the name change as shoving off colonial rule when it became Mumbai in 1995). And of course, there's good ole' political reasons like St. Petersburg/Petrograd/Leningrad/St. Petersburg.
And let's not discuss how it's Istanbul, not Constantinople. I looked at many works, but it seems the Historians Jimmy Kennedy and Nat Simon suggest it's nobody's business but the Turks', which was further backed up by other people who Might Be Giants in their field. It probably is the same reason why old New York was once New Amsterdam (Actually, it was the change of the official language resulting from the change of official government who controlled the city).
Suffice to say, names of places change over time and through languages for all sorts of language and the response to learning these changes can range from offense to "meh" and everywhere in between.