Best plot twist ever ! I never saw that one coming...
Here is my theory :
After coming back after 6 years, Cha Joon Pyo found out his wife, Min Seo Yeon, came back as well with a daughter, Do Hyun, claiming she's his. (Actually, the real father died so this was her only way to find shelter for her and her daughter.) Do Hyun was therefore put in the family registry under the name Cha Do Hyun. While he was away, Joon Pyo also had a son, Shin Se Gi, with another woman, Shin Hwa Ran. Not divorced, he didn't officially recognised his son but still brough him into the house. Then he discovered the girl wasn't actually his daughter.
At this point, some "accident" happened to Min Seo Yeon, who wanted a divorce, and she died. In the basement, Se Gi told the girl Do Hyun that his "mother" was Min Seo Yeon because she was his father's wife, so step-mother actually.
Ashamed, to cover up his wife betrayal, Cha Joon Pyo decided to hide the girl in the basement and raise his son under Cha Do Hyun's name. So Se Gi had to live using Cha Do Hyun's name AND be a perfect heir for his father, otherwise the real Do Hyun would take the beating in his place. This is the root of his DID. After the fire incident, Se Gi snapped and run away from his past by becoming the "perfect heir Cha Do Hyun", who knew absolutely nothing of what happened then. But, over the years, his DID developped other personalities, becoming less and less controllable. In the end, the "perfect heir" still had to run away to the United States to cover up his illness, convinced he was the original one.
Well, as we can see in the last episode, his personalities seem to merge together now ^^
