Koreans, no doubt, have many customs and traditions that govern the naming of people, places and things. I don’t pretend to understand all, or even many of them, but let me relate a few that I have observed.
As for people, most Korean names consist of a monosyllabic family name and a two-syllable given name. The “John Doe” of Korean names is, for some reason, 홍길동 (Hong Gil-dong), a legendary bandit leader and advocate of the people (often likened to Robin Hood) about whom at least two dramas have been made. 홍 is his family name, and 길동 is his given name.
Like most Korean names, 홍길동 is a Hanja-based name. Hanja (한자, pronounced 한짜) are Chinese characters, as used in the Korean language. 한자 is analogous to kanji in Japanese, except that as a rule, 한자 are used as rarely as possible, whereas kanji are used as frequently as possible. 한자 are used mainly to abbreviate (e.g. 韓美 = Korea–U.S. relations) and to disambiguate (도 can be island, province, street/way, and many other things; 島 = island, 道 = province, 途 = street/way). In the case of names, 한자 serves to disambiguate, and thus, add meaning to the name. In 홍길동’s case, his name is written in 한자 as 洪吉童:
洪: broad, wide, vast
So his family name means “wide,” which can be interpreted as “widely known,” or famous. And his given name means “lucky child.”
There are definitely exceptions to this custom. You may encounter people with two-syllable family names and/or monosyllabic given names. But this is rare, and in any case, most Korean names will have 2-4 syllables in total. Most, but not all names have 한자 roots.
Similar customs apply to place names. Most place names have two syllables, excluding suffixes like 산 (mountain), 도 (province… or island… or street/way…), with each syllable derived from a 한자 character. Here are some examples:
인천: 仁 (“benevolent”) + 川 (“stream”)
강남: 江 (“river”) + 南 (“south”)
종로: 鐘 (“bell”) + 路 (“street”)
Notably, 서울 (Seoul) is not a 한자-based name. Words and names without 한자 are referred to as pure Korean.