Wikipedia
Bon-gwan is the concept of clan in Korea, which is used to distinguish clans that happen to share a same family name (clan name). Since Korea has been traditionally a Buddhist country, this clan system is cognate with Gotra in Sanskrit texts and shares most features.
A Korean clan is a group of people that share the same paternal ancestor and is indicated by the combination of a bon-gwan and a family name (clan name). Subsequently, a bon-gwan is treated as though a part of a Korean person's name. The bon-gwan and the family name are inherited from a father to his children, thus ensuring that persons in the same paternal lineage share the same combination of the bon-gwan and the family name. A bon-gwan does not change by marriage or adoption.
Bon-gwan are used to distinguish different lineages that bear the same family name. For example, the Gyeongju Kim and the Gimhae Kim are considered different clans, even though they happen to share the same family name Kim. In this case, Gyeongju and Gimhae are the respective bon-gwan of these clans.
Different family names sharing the same bon-gwan sometimes trace their origin to a common paternal ancestor, e.g. the Gimhae Kim clan and the Gimhae Heo clan share Suro of Geumgwan Gaya as their common paternal ancestor, though such case is exceptional.