I suggest looking for the old surname first.
Kim:
The earliest surname of China used by Manchu people was Gulun, and that of China people was Jin. According to the North Korean ancient book "A Record of the Li Dynasty", the Nuzhen governor in the north of Tieling lost thousands of houses and posts, and took Jin as his surname.
The old surnames are: Ai Xinjue Roche, Jin Jiashi, Jingji, Jinggeli, Solz, Niu Zhilu, and Jin (Korean, Han) who entered Man.