I wrote the following off the top of my head, with no fact-checking. If you have any information or views regarding the matter, you are even more welcome than usual (if such a thing is possible) to share them here.
RD writes that the Chinese in Taiwan, Hong Kong and Singapore routinely take on Western first names, and some mainland Chinese do it as well, while Koreans rarely do that. And it is also true that members of the Chinese diaspora have taken on local names in many places in Southeast Asia (Thailand, the Philippines, and Indonesia come to mind; Malaysia, less so, unless they convert to Islam) while usually maintaining their Chinese names as well, even after multiple generations. Do the Chinese blend in better than the Koreans?
However, the perceived difference between the Chinese and Koreans may only be a historical accident. The majority of pre-WW II Koreans who were compelled, politically or socially, to take on Japanese names after the occupation and annexation but stayed on (or in some cases moved into) Japan after WW II retained their Japanese names (though in custom only: I’m sure the Korean authorities would not issue passports under Japanese-sounding names) did not revert to their real names until many, many years after the war. In fact, a large number continue to use their Japanese names. We all do what we need to do in order to blend in, though the Chinese appear to do a good job of maintaining their Chinese identity*.
(sidebar: In contrast, I think that we Japanese tend to melt into the scenery after the first generation. It’s probably relevant here that Japanese surnames not of samurai origin are heavily geographical and/or topographical. Also informative, a Philippine diplomat once noted that Philippine and Japanese ex-pats and immigrants, unlike most other immigrant groups, do not form enduring clusters.)
Whence the Chinese custom of adopting English first names? I have no way of proving it, but I suspect that the Hong Kong people (Hong Kongians? Kongese? Kongites?) and Singaporeans began doing it under British rule, and it spread to the Taiwanese when they moved closer to the U.S. during the Cold War*.
I think that there's also a generational factor mixed in somewhere, probably in the first decade or so after WW II, when anti-Asian racism was still overtly present in Western society. You'll probably find that fewer Japanese businessmen adopt those Anglo nicknames (Tad, Bud, but never Miguel, never Juan) these days. So the generational factor may be a major reason that the custom is far less prevalent among the late-emerging mainland Chinese. (Chip-on-the-shoulder nationalism could be another, but I don’t think it is a major factor.)
* For what it’s worth, I’ve been told by NW, a young Taiwanese who studied in the US, that the Taiwanese usually choose their English names when they file for a passport though some do get them earlier.
…okay, back to work…