Myungsoo or L? What's the big deal? It's just a person with two names. Even different name they are still the same person. The dorky and charming boy and many more. No matter which name he goes with, Myungsoo or L, he is still the same person. If ask me to choose, nope, not going to choose, I prefer both. No matter what, Myungsoo and L will always be my choice. 

P.S Don't bother. Just letting out my opinion because come across some one talk about his names and in related with his 'split personality'? For me it is not a split personality, it's just him and only him.