Why do Koreans and Vietnamese have the same surnames as China?

In fact, many of them immigrated from China. Many Koreans and Vietnamese clamor for their territory, including vast areas of China. In fact, in the final analysis, they "still cling to their homeland." The "homeland" mentioned here is the place where their ancestors grew up, because they are descendants of China and sons and daughters of China! Do you know that the ancestors of South Korean President Roh Moo-hyun and former President Lu Taiyu (whose direct ancestor is Lu Zhi from Zhuozhou, Hebei Province) are Jiang Ziya from China, the ancestors of current UN Secretary-General Ban Ki-moon are from Fujian in China, and the ancestors of president Chen Deliang in Vietnam are from Fujian in China? There are several sources of Korean Jin surname, the first one comes from King Silla Jin Kunzhi, and the second one comes from King Kaye Jin Shoulu.

South Korea's Park surname comes from Park He Ju, the ancestor of Silla King (although Silla King belongs to the same family, there are two surnames: Park and Kim). Both surnames belong to surnames from ancient myths and legends. In addition, the surnames of Gao, Fu and Liang in Jeju Island are also derived from myths and legends. Fu Xi, king of Baekje, and Gao Shi, king of Koguryo, all took their surnames. There are also some surnames given by the ancient Emperor China or the kings of the three countries on the Korean Peninsula (such as Jinhai Xu Shi given by King Silla and Ganquan given by Emperor China), and they changed their surnames (after the demise of Korea, the Wangs changed their surnames to Yu, Quan and Tian, etc.). Fu Yulong, the son of Baekje Yici King, went to study in the Tang Dynasty after his death and was given the surname Xu. After Silla, the third generation Confucian king, divided the country into six tribes, he gave the chiefs of each tribe surnames, such as the surname Sun given by Zhu Lima, the surname Cui given by Suvaduri and so on. There are also insulting surnames given by the king to "disorderly people", such as ox, horse, elephant (later changed to Shang), roe (later changed to Zhang) and dolphin (later changed to Dun). There are also some ancient surnames of unknown origin, such as Xianyu, Xu and other surnames handed down from Korea founded by China. During the Warring States Period, China immigrant Chen Han handed down the Su surname, and Chen Han's descendant Baekje's "eight surnames"-Sha, Yan, Xie, Guo, Zhen and Miao.