LORELAI: Young-Kwan, good to see you. Hee-Jin, hi. Oh, I love your hair. Su-Nam, hi. Hi. Ho-Kyung, Won-Kyu, great to see you, hi.
Young-Kwan – a male name meaning “brave and strong”. In A Year in the Life, one of Lane’s sons is named Kwan, so it is possibly a family name.
Hee-Jin – a female name meaning “precious pearl”.
Su-Nam – a male name which can be translated as “man of a long lifespan”. Lane said she had a cousin called “Nam”, I am not sure if this is the same person or not.
Ho-Kyung – a unisex (?) name which can be translated in several ways, including “bright and respectful”.
Won-Kyu – a unisex (?) name which can be translated as “first and standard”. I have only ever seen it the other way around, Kyu-Won, when it is usually male.
Notice how familiar Lorelai and Rory are with the Kim relatives, knowing their names, and comfortable enough to make polite small talk. They look genuinely happy to see Lorelai and Rory. Although we rarely see it, the Gilmore girls must often attend family gatherings at the Kim household.
The Kim family members are played by Peter Kim, Jennifer Bolton Lee, Janet Song, Kim Kim, Alexis Rhee, Greg Joung Paik, Jae Woo Lee, Sunny Bonner, John D. Kim, and April Moon. None were very experienced at this point, but Rhee and Song have gone on to have long careers, appearing in some well-known and popular productions.
Note: I know nothing about Korean names, so feel free to rip this apart!