Mainly because North Korea was a vassal state of China at that time. And deeply influenced by China culture, they adopted the concept of Chinese civilization in etiquette and even clothing. China's Chinese characters are even used in surnames and characters. Although there are not many Chinese characters left in North Korea due to the evolution of removing Chinese characters. But we can see that many famous calligraphers in North Korea or South Korea write in Chinese characters. And these three surnames are all from the royal family, so they are very distinguished.
Although some people's surnames are very similar. But they are usually distinguished by their ancestral home. So although they may have the same surname, they come from different ancestral homes. Of course, this is a different understanding from China culture. Because China culture advocates the principle of "one country under the world". North Korea and South Korea use names to show their dignity, which is why they choose to do so. But later, because civilians used these noble surnames too much, they chose to distinguish them by their place of origin.
Of course, this is mainly because these three surnames were used by the Korean royal family at that time. So it gradually spread and evolved into three surnames. This is also because the rulers of these three dynasties controlled this area of Korea for a long time. Therefore, many Koreans gradually adopt their surnames to express their memories.