Lan's actual name is simply C - it's Gingetsu who decides to name him Lan (Ran). He was called C because he was one of the three-leaf clovers that once existed, and those triplets' names were A, B and C. Now he's the only one living left, and as he's living away from the Clover Project research facility, he's aging quickly (that's why we can see Ran as a child in the last volume flashback, and as a boy in his late teens or even early twenties in the other volumes, even when two years have passed only since he met Gingetsu for first time). Actually, his life will end in five years - and though he knows it, he still wants to be away from the facility... and not only because he wants to be free - but specially because he wants to be next to the person who's most important to him.
Ran's character isn't much developed until the last volume either - a flashback to how Gingetsu and Ran met and their relationship began. However, Ran is different from Gingetsu: as a child, Ran is quite mature for his age; but he's innocent, caring, kind and doesn't seem to have any problem expressing his feelings. He doesn't want anyone to suffer, and is always willing to help if needed. He's sweet and nice, but not weak: his existence has been quite hard so far, and though he knew it wouldn't be easy, he decided to go for a change running away, risking his own life in search of freedom.
(Sourse: Unspoken)