I was thinking along the lines of, well, it's not as if any given country "owns" somebody's name -- it's a property of the person, right?
That's a bad train of thought. You have to think about the institutions involved. There are certain things that international law guarantees to you, that your country is obliged to provide to you.
Things like "Everyone has the right to recognition everywhere as a person before the law." "Everyone is entitled in full equality to a fair and public hearing by an independent and impartial tribunal, in the determination of his rights and obligations and of any criminal charge against him."
In this case also important: "(1) Everyone has the right to a nationality. (2) No one shall be arbitrarily deprived of his nationality nor denied the right to change his nationality."
You don't really have an inane right for two nationalities. If a country allows you dual citizenship it's a nice thing to do. As such I wouldn't expect naming right to arise as a consequence.
As in, you can't have one legal name in one country and another in some other country.
That's certainly not the case.
If I remember right you can't have the same legal name in South Korea as in Germany or New York.
In South Korea your name needs to be written in Hangul and the legal documents about you are addressed to the name in Hangul. In Germany your name has to be in the standard Latin alphabet (I don't know how much accents it allows). Quick Googling suggests that the case for China is similar. You get to choose between Simplified characters or Traditional Chinese ones.
There are certain things that international law guarantees to you, that your country is obliged to provide to you.
No, there are certain things that international law says are guaranteed to you, that international law says your country is obliged to provide to you.
You need the additional premise "if international law says a country is obliged to provide something, then that country is obliged to provide it". I see no reason to believe that premise. It doesn't seem to be true either as a statement about how countries should behave or about how countries actually behave.
Thus spake Eliezer:
It seems that many here might have outlandish ideas for ways of improving our lives. For instance, a recent post advocated installing really bright lights as a way to boost alertness and productivity. We should not adopt such hacks into our dogma until we're pretty sure they work; however, one way of knowing whether a crazy idea works is to try implementing it, and you may have more ideas than you're planning to implement.
So: please post all such lifehack ideas! Even if you haven't tried them, even if they seem unlikely to work. Post them separately, unless some other way would be more appropriate. If you've tried some idea and it hasn't worked, it would be useful to post that too.