Kim: Kim (occasionally romanized as Gim) is the most common surname in the Korean Peninsula and among the Korean diaspora. The hanja (Chinese character) for Kim is 金, meaning "gold". The Korean pronunciation varies: as a common noun meaning "gold" or "metal" in general, it is pronounced [kɯm] (금, geum), but as a surname or in place names,[1] it is pronounced [kim] (김, gim). Kim is the most common family name in Korea. Park: Park is a notable Korean surname, traditionally founded by King Hyeokgeose (혁거세) and theoretically inclusive of all his descendants. In Chinese characters (Hanja), it was written as 朴; in Hangul, it is written 박. The name "Park" is usually assumed to come from the Korean noun 박 bak, which means "bottle gourd," or the Korean adjective stem 밝 balk-, which means "bright." Lee: Lee is the common English spelling of 이. 이 is derived from the Chinese Hanzi character (the Korean Hanja character is written the same way) 李 is the second most common family name (after Kim)김 in Korea, with 이 derived from 異 or 伊 being relatively rare. The hanja 李 literally means "plum" or "judge." This character, as used in Korea, China and Vietnam, is the the most common surname in the world. Refer to https://en.wikipedia.org/wiki/Kim_(Korean_surname) https://en.wikipedia.org/wiki/Park_(Korean_surname) https://en.wikipedia.org/wiki/Lee_(Korean_surname)

Nowadays almost all Korean people couldn't care less about heraldry. The new ruling class emerged less than a century ago, those who amassed massive wealth and power through capitalizing on industries during Japanese occupation and post-Korean war boom era. None of these guys claimed noble lineage, probably because they don't have one. Commerce and industry were looked down upon in Joseon dynasty, and instead the nobles busied themselves discussing philosophy and other arty-farty stuff, so these guys are probably from commoner class or even the slave class. AFAIK similar thing happened in China, where sino-russian war, sino-japanese war, ww2 and communist revolution pretty much destroyed everything in the old system. I hear things are quite different in Japan, which is interesting. They still have old noble families that date back hundreds of years, has huge estates, and dominate local elections where it's not very uncommon to see son or daughter of the former politician succeeding their parent's post. My family, Yeon-An Yi(Lee)-Ssi, traces its roots to Tang general Yi Mu, who settled in Korea during late Shin-La period (~900 AD). Many great ppl were born into this family and attained highest positions in government during Joseon dynasty. Nowadays, there are hundred-thousand of us, and most are pretty average, normal ppl.

Then cities got larger and even the place of origin addendum wasn't enough to distinguish between different families. There might be several Kim families in large cities. So they came up with different "clans" within the clans to identify their lineages. This practice was quite notable during Joseon dynasty - which isn't medieval kingdom actually; it existed from 1400~1900 and was quite advanced for monarchy, and the king shared quite a bit of power with the court and ruled by law, but anyway - and because Joseon was very long-lasting dynasty(500+ years), many great families emerged and perished during this period. Often when someone of noble class entered into King's service and attained some super high position in the government, he'll receive honorific title of "something-something-'Gong'(closest english equivalent would be "lord")", and he'll have an option of going on to create a new branch of the family and become a founder of that clan(or faction). An example would be "Gyong-ju Kim-ssi Bu-sa-gong-pa", which roughly translates to Lord Busa clan(or faction) of the Kim family of Gyong-ju. Anyways, the fall of Joseon dynasty(and short-lived Korean Empire), Japanese occupation of Korea, and ensuing Korean war changed all that. Beginning at the late Joseon dynasty, common people started using surnames (most often just borrowed from other noblemen), and the practice of wealthy merchants from humble families buying their way into noble lineage (either through marriage or outright forgery of genealogy tree document(called Jok-bo)) became commonplace. Shortly after, many noble, ancient families were left in ruins, Korean war being the greatest contributing factor.

I know this question is couple of years old, but I felt the "best answer" below doesn't really address OPs question and figured I'd chip in. It's a really good question, but more often than not your typical average Korean may miss the point entirely because they lack understanding of how surnames are in other countries and fail to grasp where questioner's coming from, and/or not very familiar with Korean history themselves. Kim, Lee, Park are by far the most common surnames in Korea. One in five Korean is Kim, one in seven Korean is Lee, and about one in ten Korean is Park. Following closely in fourth and fifth are Choi and Jung (sometimes romanized as Cheong, Chung or Jeong), and these five surnames account for more than half of Korean population. So the answer to your first question is yes, these names are indeed quite common. There are another two dozen or so of common surnames, that average Koreans are familiar to seeing in day to day life, such as Kang(Gang), Go(Ko), Na, Nam, Min, Bang, Bae, Baek, Byeon, Seo, Son, Song, Sin, Sim, Ahn, Eom, O, Wang, Yun, Im(Lim), Jeon, Jo(Cho), Jin, Cheon, Pyo, Han, Hong, Hwang, .. etc.. Outside of these and maybe few others, rare, unique surnames are quite rare such that when Koreans see one that they've never seen before, they'll know it doesn't "sound like" a real name. In the old days, similar to many parts of the world, average Koreans(i.e. peasants) didn't have surnames and weren't allowed to have one. But even among the ruling class it was quite common that they have "same" surnames. The way they distinguished themselves into separate "families" is by identifying the town/region they're from. So instead of simply saying someone is Kim, they'll say he's from "Gyong-ju Kim-ssi", which roughly translates to Kim family(Kims) of Gyong-ju. In feudal Korea small villages usually contained only one (extended) family of each surname, so this system sort of worked.