You can tie yourself in knots about what to call foreign countries and people, or you can just say, "Sod it, I'll use whatever word I want." One should be sensitive to other people's feelings but one can't be totally governed by them. For instance, I've been told that Turks want us to call their country Türkiye, as they do, but all three of my Turkish friends call it "Turkey" when speaking and writing English. Similarly, I'm told the Dutch don't like being called 'Dutch' (see the Twitter exchange on the right), but what's the alternative?
There are 80 million people in Turkey and 17 million in the Netherlands. Chances are they don't all have the same opinion, and many of them probably have no opinion at all on what you call them or their country. Don't worry about it.
Other countries are more sanguine. No German would expect an English speaker to call his country Deutschland, and the Japanese are quite happy that we don't call them Nihon-jin (Nippon is also correct, but terribly old-fashioned, like calling England 'Albion'). And, boot on the other foot, what's the Japanese word for 'English person'? Do you know? Do you care? (It's 'Igurisu-jin', if you must know.*) Are you, if you're English, going to insist on the correct term? Of course you're not. In some ways, I'm flattered that they have their own word for my country and language. It suggests it's important to them, and what could be more flattering than that?
Tying yourself in knots will leave you like the hapless Guardian newspaper, which is so desperate to be correct that it can't see any kind of perspective. Look at this exchange from a live report of a cricket match in India in 2011, in which the writer reports the events of the match while fielding emails from fans (not just any cricket match, but one of the greatest ever World Cup matches):
Subsequent overs report other readers' comments, including a bemused Sriraghavan B: "I am from Madras, India and I still call it that way as do many of my relatives, neighbours and friends and many more. It never occurred to me that I should say Chennai as I feel that it is not right."21st over: India 116-1 (Tendulkar 44, Gambhir 33) Five from Yardy's over: two singles, a two and a wide. England have got to take wickets in these middle overs or the death overs could be extremely painful. "Please stop calling it Bengaluru," says Robin Percival. "The English name for the city is Bangalore; just as the English name for Roma is Rome or Moscva is Moscow. I have just returned from spending over five weeks in Bangalore and everyone I spoke to (in English) referred to the city as Bangalore. Of course I do not speak Kannada and if I did I would call it Bengaluru. English language papers in India such as The Hindu refer to the city as Bangalore. Why can't the Guardian?" Don't shoot the style guide adherer. I know I am a maverick, but I will never – never – deviate from the Guardian style guide. My life would not be worth living. (Guardian, 27 February 2011)
And God help you if you call all Eskimos Inuits, because most of them aren't. I'm sorry for pasting this whole exchange, but the relevant episode of QI isn't on YouTube and you'd have to register with the website to read it in its original location:
The word "Eskimo" is non-PC in Canada, much as it's fine in Alaska. The particular indigenous person of the north who was featured on QI was a Yupi'ik from Alaska - Sarah Palin's husband is one of those as well - and hence "Eskimo" rather than "Inuit" is the term to use. The plural of Yup'ik is Yupiit.(And for those who are interested, here's a case study from QI on how they got the question about Jerusalem - the song - wrong.)
Had the person been an Aleut, then again "Eskimo" might have caused offence. The Aleut are very sure that they are not Eskimos; while they don't object to "Aleut", they prefer one Unangax̂, two Unangax, three or more Unangan. (Note that most of the Eskimo-Aleut languages have what's called a dual number; this comes between singular and plural and is used when there are two of something. It's rare in European languages; Slovenian and Sorbian have it, and it's on the point of vanishing from Lithuanian.)
The indigenous people of Baffin Island and such like places absolutely are Inuit, although "an Inuit" or "lots of Inuits" are always going to be wrong since "Inuit" is the plural. One Inuk, two Inuuk, three or more Inuit.
While the people of the central Arctic would prefer Inuinnaq to Inuit, they won't get especially upset at the more general word. As for indigenous Greenlanders, the preferred term is Kalaallit, singular Kalaaleq. (There's no dual in Greenlandic.)
The Guardian style guide might try to do the right thing by pressure groups, but if none of its readers understand what it's talking about then surely it has failed. The readers make their own rules, not always logically, so Pinyin spellings for Chinese names have largely been accepted ('Beijing' instead of 'Peking', etc) while only 'Mumbai' of the new Indian names has really caught on.
I've said this before and I'll say it again: whatever you write, you write for your readers. As soon as you put anyone else's interests before the interests of your readers, you've abandoned your responsibilities as a writer.
Moral: If someone else has their own word for my country or language, I'm not offended. I'm flattered.
* No it isn't. See the comments.