it's a property of the person, right?
Nope. Your relationship to your name doesn't fit most of the bundle of rights that the word "property" implies.
you can't have one legal name in one country and another in some other country
Of course you can. Why not? Consider immigrants who acquired a new citizenship but did not renounce their old one -- the names on their two sets of papers do not have to be identical.
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.