Re: “Islas Malvinas” (the unofficial, Argentine, name of the Falklands)
If the government is not democratically elected, but is recognised internationally, then it gets to do the naming. If there's a genuine dispute, rather than just a few people objecting who mostly get ignored, then you get weird no-right-answer conditions. Which has always happened.
There is, and can be, no perfect solution. And the UN has to try and get stuff done, so tries to have standards. But this does lead to ludicrous situations like having a country called "The former Yugoslav Republic of Macedonia"
The process is a bit weird with non self-governing territories/dependent territories. Because they haven't really gone through the same international recognition that a country has - so there's an argument to say that nobody can give them an official name, since nobody has been recognised to do so.
Like lots of international law, it comes down to there being nobody to enforce any decision made, so there is no real answer. Partly because there's no mechanism to deal with 2 different bits of international law being incompatible.
So OK, nothing is official. The UN decolonisation committee's final answer at the moment is that there need to be talks over sovereignty (presumably in order to give Argentina a chance to colonise the place?), so looks like there'll be no solution for a while.
But lots of countries recognise the Falkland Islands government. They call it the Falkland Islands. That's the official name. It's as official as anything you can get. As with much law, it's all just legal opinion until you can get a court to decide the right answer.
I don't have any jingoistic preferences by the way. Just an interpretation of a murky legal situation. If you're speaking spanish, it's the Malvinas, Malouines in french, Falklands in english.