I am by no means an expert, but I can share what I know about my mother-in-law's family (which is very little). My MIL's birthplace is listed as Seoul, Korea. Her father was killed during the war when she was a very small child (2-3). I do not know if he had an occupation aside from being in the military.
She and her mother both have the same second syllable name: In Sun and Il Sun.
Her four brothers all have the same first syllable name: Nae Yuan, Nae Chan, etc. (can't remember the other two off the top of my head)
So if there is a visable naming pattern for your characters, I would imagine it would be between mother and daughter. Wives keep their name and children take on their father's surname. I remember this because when I addressed wedding invites I had no idea this one person was her mother, because she did not have the "Pak" surname.
ETA: I found this at Wikipedia and explains why the brothers all have the same first syllable name:
The family name is typically a single syllable, and the given name two syllables. There is no middle name in the Western sense. Many Koreans have their given names made of a generational name syllable and an individually distinct syllable, while this practice is declining in the younger generations. The generational name syllable is shared by siblings in North Korea, and by all members of the same generation of an extended family in South Korea. Married men and women usually keep their full personal names, and children inherit the father's family name.
Here is the link.
http://en.wikipedia.org/wiki/Korean_name
So based on this information, the surname of the daughter needs to match that of her father. And then you could do like my mother-in-law and her mother and have the second syllable of their names the same to show some sort of connection between daughter and grand-daughter since their surnames would not match.