Why doesn’t everybody, for example, call Germany what the Germans call their own country, Deutschland? Doesn’t seem that hard for anybody else to learn-is there an etymological reason why?
Yes, the Latin word Germania for that area is a lot older and, since the Deutsche don’t mind, the rest of us go on calling them and their country by whatever happens to be their traditional name in our languages.
In other languages it’s Allemande, Alemania… which according to this Chilean site comes from an Old German word meaning “all men” (a better translation might be “all the People”).
Wiki has a good overview of how Germany got its varied names; some call it after the Alemanni tribe that lived in Germany, or a bit of it, we get it from the Romans who called the inhabitants “Germani”, a term probably meaning related (in this case to the Gauls), the Germans themselves get it from the Old High German “diutisc” meaning people, in Eastern Europe they’re named after the Saxon tribe, the slavic word derives from a word roughly meaning ‘someone who speaks a foreign language’.
Wiki keeps saying that the official name is “Federal Republic of Germany” and then they give the German version (Bundesrepublik Deutschland). Does Germany have an official English name (that is, is there a German law somewhere that officially states that Germany’s name in English is “Federal Republic of Germany”)?
AFAIK they haven’t bothered define in a law what they should be called in other languages (there’s a lot of other languages!). But in English-language documents, they refer to themselves as the Federal Republic of Germany. Doesn’t get much more official than an embassy.
The name is Germania in Italian and Russian, Doitsu in Japanese, Deguo in Chinese, Alemania in Spanish, Saksa in Finnish…
The only case I can think of, of a country insisting on being called anything in a foreign language, is Cote d’Ivoire, which used to be called Ivory Coast in English, but English speakers acceded to their demands that they use the French name for the country.
At the heart of the question, the answer is this: Names of countries are just words, and there is no reason to expect this kind of word to remain constant across languages, any more than the word for “pencil” or “book”.
It’s not realistic to expect the names of countries to remain constant between languages. After all, personal names don’t and for the same reasons. One of those reasons is that different languages have different rules for how syllables and words are constructed. What’s perfectly acceptable in a particular language may not happen at all in another particular language. An example of a personal name (in this case, a surname) sounding different is the Vietnamese name Nguyễn. The “ng” at the beginning is not a possible word beginning sound in English; however, it’s quite common in that position in Vietnamese. English speakers generally speak the name as though it’s Gwen or Win.
Speaking of Vietnamese, when I was learning that language at DLI, I got a kick out of the Vietnamese word for America: Hoa Kỳ (Flower Flag/Flower State).
Also Cape Verde/Cabo Verde and East Timor/Timor-Leste.
There have been a few other places. We used to call Beijing, Peking, and Mumbai, Bombay for example.
Myanmar insisted on using that name instead of the old Burma .
Cambodia had the name Kampuchea applied by the Kmer Rouge .
Thailand has thrown off the exonym (or epithet ) Siam. (Sankrit for brown… )
Sri Lanka has thrown off a number of names such greek Taprobane, arabic Serendib ( origin of the word serendipity) , portugese Ceilão, and the english Ceylon.
In the Magyar language, Poland is called . . . Lengyelorszag.
And let’s not forget that, in English, the Magyar language is called Hungarian.
The country of Georgia is called Sakartvelo (საქართველო) by the people who live there.
That is not necessarily applicable to proper names. My legal name is “just words”, and any form other than that on my legal documents of identity at my place of origin is wrong and cannot be justified. Allowances made only for languages that use a different alphabet, but they are restricted to the closest phonetic approximation in their alphabet.
For example, if my legal name is John, and I immigrate to a Spanish speaking country, my legal name does not become Juan.
Back to names of places. Modern countries are pretty much known by the same name everywhere , with allowances made in a few cases for non-existent phonemes, or endings that need to be changed to validate the name to be declined as a noun. or whose names contain a common word (south, new, republic, etc.). But countries that have been in existence for centuries have acquired names in various languages, according to the diplomatic customs of previous eras, which are now too well vested to change, and not many English speakers are eager to learn (and pronounce) names like Sverige or Misr, when they can’t even find the places on a map using their customary names.
Not unless you want it to, you can change it. My full name includes a four-word firstname, three-word first lastname and one-word second lastname, and even reducing it to four words (abbreviated firstname plus first lasname) causes so many headaches in non-Spanish/Portuguese speaking countries that I would never try it. Keeping one’s second lastname when moving to an English-speaking country is a very recent development. I’ve received plane tickets issued to a Mrs. De (that’s the third word, so “of course” the lastname, right?).
I didn’t realize the Magyar people spoke the dark language of Mordor. 
The name United States is not really a name; it is a description and is translated in the languages I am familiar with: Etas-Unis in French, Etados Unidos in Spanish, Vereinigten Staaten in German, and so on. The individual states do acquire declensions. My birthplace is Philadelphie, Pennsylvanie in French, for example.
And in Italian, the Germans are called tedeschi, so the name of country and people don’t match. Spanish also has tedescos, but most people wouldn’t know what that means; RAE doesn’t have tedesco but has tudesco for an area in Southern Saxonia and its people, they give its origin as coming from medieval Latin teutiscus and this from Germanic Thiudiska.