Many systems in China depend on your Chinese name and identification number. Suffice it to say, foreigners who work in China don't have either of these: a made up Chinese name is not meaningful or legal (China also lacks any kind of kana), a passport number is not a "valid" ID number and changes every 10 years anyways. I don't get to use many online services accordingly, and every year there is some problem with how they handle my last name (MC DIRMID, there is a freaking space after the MC in my passport, causes all sorts of problems).
When I worked in Taiwan they came up with a Chinese name for me and gave me a little official wooden stamp I could use to "sign" official documentation. The name was indeed useful to fill in all sorts of forms that expected the Chinese format. That was a neat time.
It's meaningful in some contexts. I had a different Chinese name on my work permit and marriage certificate (in both cases transliterated without my input), and it caused me no end of hassle when I was applying for a mortgage - we got refused the first time and had to get the work permit changed to make them the same.
Yes, we (my wife and I) were careful about that when we got married last year. But to be honest, I think that's the only case (and the name on my work permit is not even my own chosen Chinese name!)
Tibetans (with Hukou anyways) have Chinese names though. Usually they are phonetically chosen. Its something that must be done when you are born in China I guess, even if your native language isn't Chinese. This applies to all minorities who use different writing systems (Uigher, Manchu, Mongolian, etc...).
Japanese of Korean descent can also choose Kanji names I think, to use as legal aliases.
Anyone who lives in Japan can register a legal alias, regardless of their citizenship. The special permanent residents that you mentioned (who typically hold North / South Korean or Chinese citizenship) are probably the most common users, but some Japanese people who are divorced use them, too.
An alias with Kanji is really useful for living in Japan. I'm an American citizen but I use an alias with a Kanji last name for just about everything I can (including my job, bank account, and apartment contract). Immigration paperwork and credit cards are just about the only things where the alias can't be used.
