Yes, and imagine the impact this has on "foreigners who work in China" such as Tibetans in Lhasa.
Japanese of Korean descent can also choose Kanji names I think, to use as legal aliases.
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.