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). Since it is important in Korean culture to know exactly which clan one belongs to, a Bon-gwan works as if it is a part of a Korean'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.
Restriction on marriage and adoption 
Traditionally, a man and a woman in the same clan could not marry, so the combination of the bon-gwan and the family name of a husband had to differ from that of a wife. It had been also prohibited by law until it was ruled unconstitutional in 1997.
On the other hand, when adopting a child, the adoptive father and the adoptive child must belong to the same clan. Therefore, they must share the same combination of the bon-gwan and the family name. Parents used to prefer children from the same clan, but recently the clan or family name isn't a deciding factor in adoption. It is due that now it is legally possible to adopt a child from a different clan and change the child's family name.
Full list of survived Bon-gwan 
It's possible for Korean nationals and Korean descendants to look up their own bon-gwan. List of survived and newly created bon-gwan can be view from below web link.
 List of Korean bon-gwan (available only in Korean language)
 List of Korean bon-gwan (In Russian and Korean languages)