It's a common knowledge that the names of many celebrities out there are not their real names. The same goes for some of the Korean stars who I fervently follow as a fan.
Korea Times story - How Stars Creat Their Names provided some interesting nuggets of information on how some of the stars which we follow got their names.
Take for example, Gong Yoo, of Coffee Prince fame, created his name by putting together the last names of his parents, Gong and Yoo. Having a name that represents his parents allowed him to work twice as hard and take responsibility for his works. Isn't that sweet?
As for Rain, he got his name from a producer whom nicknamed him "Rain" since the skies invariably poured whenever Rain was recording his songs. Guess Rain makes for bad company on his recording days since chances are likely that it is, cold, wet and 'rainy'. Then again, fans of Rain wouldn't mind spending time with him even if a typhoon is coming down the street! So what's some rain to them when they have Rain with them.
Lastly, I am sure stars choose a name which is memorable and easy for fans to scream it. Take Hyun Bin for instance. The name Hyun Bin exudes a certain sense of urbane sophistication and coolness. Would Hyun Bin fame be still as good if he used his real name - Kim Tae-pyeong? It would kinda weird to hear people shouting "Kim Tae-pyeong, We Love You!"