Why Do Koreans Have The Same Names?

I've noticed a lot of Koreans have the same names. For example, there are 3 actors with the name Kim Soo Hyun, and 2 with the name Lee Min Ho. There's a lot of Min-Hos as well in idol groups. If there is so many same names within the celebrities, imagine how many more if you include the names of the Korean public. Why is that? Are they not creative enough and run out of names for their kids? Or unless, it's bad English translation. So many Kims and Lees as well. I guess it's the same in Chinese, so many Wongs and Lees. But, at least in Chinese, you don't have so many actors with the exact same names ^^

Kim So Hyun 1999

Kim Soo Hyun 1985

Kim Soo Hyun 1988

Lee Min-Ho 1993

Lee Min Ho 1987