Xion was created from Sora's memories of Kairi, that is why she looks like Kairi, and if anyone notices Saix calls Xion a puppet, multiple times in 358/2 Days, and her purpose was to duplicate the power of the Keyblade so they would have 2 Keyblade weilders, and she was also created to prevent Sora from waking up. However, Xion and Roxas shared the same power, so usually one was always weaker than the other, so the Organization decided they could only use one of them, so the Organization tricked Xion and Roxas into fighting eachother, but Axel stopped them before one of them destroyed the other. At the end of the game when you fight Xion, she is trying to absorb Roxas so she can rejoin Sora and Sora will wake up, because they both hold some of Sora's memories. Also, if any of you are wondering why Xigbar sees her as Ven, it is becuase who a person sees her as is based on that person's own memories, so if you have completed Aqua's or Ven's story in BBS, then you will know why Xigbar sees Xion as Ven.
Also, about the thing with all Nobodie's names just being their original name scrambled up with an X in it, that isn't necessarily true, Namine isn't Kairi's name scrambled up with an X in it.