Beakje was known as Kudara to the Japanese and after the fall of Beakje refugees settled near present day Nara (Japan) and founded a town called Koryo which still exists to day.
Silla on the other hand was not directly related to either Beakje or Gogoryeo. It is indigenous to the Korean peninsula. However, over time they did share close cultural and familial ties particularly with Beakje.
The people of Korea today are mostly descended from Silla, hence why there are so many people with the surname Kim and Pak.
Goryeo surnames like Go and Hae and Yeon are not as common in modern Korean society although they do still exist so it is fair to say that modern Koreans are descended from all 3 kingdoms.
Interesting story.
It is believed that Ancient Japanese had had very close relationship with Baek Je.
Family names of today seem to have not so close relations with 3 Kingdom area.
Family name in Korea was widely accepted in approximately 8 century.