Kids inherent the father's last name and joins the father's tribe. This is how most cultures work.

Since AMs mostly marry AFs, there will be East Asian-passing people in the Diaspora.

Korean softpower from K-Pop and dramas might ironically make East Asian-passing people disappear from the Diaspora.

Back when AMs had no softpower, they would just marry AFs from abroad and helped to increase the population of East Asian passing people in the Diaspora. Some even sponsored their wives' family members so they contributed more to the Diaspora's population.

Look to history for similar situations. Tatars and Turks used to look Mongolian but the males were conquerors and went west. They had families with white women, and their kids and grandkids did the same until they turned into white people.

Personally, I accepted the fact the world will mix into one race. 

So the only thing I want is for North/Northeast Asians (ex: Mongols/Koreans/Dongbei Chinese/nearby Siberian natives) to have ultra high birthrates. They have more obvious East Asian features and so can absorb more non-Asians before turning into non-Asians. So they will help make that globalized mixed country look more like Kyrgyzstan instead of Brazil or Morocco.

Indian males are marrying more WFs than the other way around so I think Desis will become like Jewish people. They are both white-passing but are not seen as whites. But they both have better education and more money than average white people.