Who knows the origin and history of the surname "Han"

Neither Ganjia Surname nor Chinese Surname Dictionary records Han surnames. There is only the sentence that "Han is a descendant of Liu, and the other is the translated surname of Ligustrum lucidum, which entered the Central Plains in the Yuan Dynasty". According to the Records of Yulin County, there was this surname in Yulin County, Gansu Province during the Daoguang period. A distant friend of mine [Yuxian County, Gansu Province] also made a survey. In order to verify the origin of the Han surname, I learned that there was a village with a Han surname in Rizhao, Shandong Province, and there was also a Han surname living in Gai County, Liaoning Province. The Han surname in Gaixian moved here from Rizhao, Shandong. According to the genealogy of Han surname in Rizhao, Shandong Province, the Han surname in Rizhao, Shandong Province moved from Jiangsu, Jiangsu and the East China Sea. According to my research, I think:

[1] The Han surname only appeared in the Western Han Dynasty. There is a fairy tale in our country. A character in The Eight Immortals Crossing the Sea is Han Zhongli, also known as Zhong Liquan. This character is not fictional, and his story is not groundless, catching shadows and having a prototype. According to documents such as Zi Zhi Tong Jian and Romance, the Han general Zhong was a Han general and his son was lonely. Because he saw through the world of mortals, he became a Taoist and then an immortal. The road number is Yunmian. Why did Zhong Liquan become Han Zhongli again? I think the reason is simple. In Qin and Han dynasties, although surnames and surnames were combined into one, surnames were still symbols of nobility. Zhong Liquan was born in the Han Dynasty, so it is not surprising to add a surname "Han" before Li Zhong to commemorate his father's achievements.

[2] "Wan Jia surname" said that the Han surname was derived from Liu surname, and I think it can be established. In the Qin Dynasty, Xiang Yu called himself the overlord of Chu, honored Chu Huaiwang as the righteous emperor, and made Liu Bang Hanwang. Liu bang won the world and was named "Han". Since then, the place names in China have been frequently used, including Hanzhong, Hanshui, Hankou, Hanyang and Wuhan. People in the Central Plains are also called Han Chinese, Chinese characters are called Chinese characters, and there are Chu and Han in the chessboard. The queen mother of Liu Bang's death violated Liu Bang's "white horse's Covenant" and Liu's promise not to be king. The Lushi family was named as the main person. Mi Zhu is a descendant of Liu Bang. Since then, Liu's family has been almost wiped out. Xin Cunren went incognito and fled far away. He changed his name in order not to forget that he is a descendant of the Great Emperor Gaozu. Based on the above information analysis. I think it is more likely that the Han surname evolved from the Liu surname. The above statement has yet to be proved by experts.