Family Name (Surname)

today my Chinese friend asked me how i write my name in Chinese
well i am korean
so why would he ask me how to write it in Chinese?

well Koreans used to use Chinese long time ago called Han-Moon
Chinese was used until Korean language (Han-Gul) was created in mid 1400s by King Sejong
even after creation on Korean language, Koreans learned Han-Moon
sometimes names are spelled in Han-Moon
because during translation, many last names were spelled differently
but by using Han-Moon people can see if other people who they share their last name
is in same family or not
so one of most common Korean surname is "Kim" but all the people who use the surname "Kim" are not related, one can use family history, DNA tests, or writing their surname in Chinese

as you all probably know, all Asian civilization started in China, some migrated south and colonized and created Korea, then people from Korea migrated further south and colonized a large island, thus creating Japan
some people in Korea, some in China, and some in Japan are actually blood related due to the migration that occurred long time ago, before surnames.

well i dont know how to spell my name in Chinese, but now i am curious
thankfully my parents know how to read and write Han-Moon and they know how my name is spelled.
but i am also curious about my family history
what does my family surname mean and what is our family history?
where do we come from?
are we related to other people who share same last name?

unfortunately i dont know anything about my family tree beyond my grand parents and to make things worse, i never met any of my grand fathers
i have two one from father side another from mother side
grand father from father side passed away when my dad was 4
grand father from mother side came to US when my mom was a teenager but was reported missing after LA riots of 1994

plus i cant use one of those family history thing online because my family originated in Korea and these sites are for families of US origin

i want to know...
damn
i have to do my own research and that means visiting Korea which will be in 5 years
i cant wait that long...