Not really, it depends on the person I suppose. Almost all Koreans have three syllable names made up of their family name and a two-syllable given name. However, you do find some Koreans with one syllable given names, although it's quite rare. I had one student who had a four-syllable name and I was told that that's even more rare but not unheard of. He was the only person I ever came across in my years in Korea who had a four syllable name.
Quite a lot of Koreans have Western names or a Westernized Korean name as well, if they speak English, are in business or are performers (with stage names) then they'll probably have a Western name.
Jenny, Sally, Judy, Julie and Sue are common among girls. Jin-hee is quite a common name in Korea and often these girls will choose Jenny as their English names. It's also quite common for girls to have Soo 수 as the first or second syllable of their names and so they're often just Sue in English. Joo 주 is a commonly found in girls or boys' names and again it can be the first or second syllable. Hence, Judy and Julie are common enough too. I don't know why Sally's popular but I know there's a Chinese name that sounds quite similar.
Of course, some girls (or some parents if they get their Western name when they're young) opt for more original names like Melody, Cindy or Shirley. Names with 'sh' or 'th' (especially ending in these sounds) aren't that common because they're difficult for Koreans to pronounce.
Dan/Daniel, James, Sean and Kevin are pretty common boys names. It's also quite common for boys with Joon 준 in their names not to change it and to either go by their full name in English or just to go by Joon. Jay is also somewhat common as Jae 재 is used fairly commonly in Korean names. I've noticed that some boys go by initials in English these days too. For example the football player Pak Ji-sung, could go by JS
There's a bit of a generational difference with names as in any other country too. For example, it's not uncommon to find 식 shik as part of an older person's name but you'd rarely find a kid with shik in their name.
It's common enough for foreigners to be given names that are somewhat attributable to their personality or bearing as well, if they have close Korean friends or have immersed themselves in Korean culture. Usually names are given when out drinking with friends though! Mine is 김채윤 Kim Chae-yoon which doesn't mean anything (Korean names usually mean something. I had a friend who's name meant "Dragon Water") but it means something to me because it's parts of my favourite students' names kind amalgamated together!