Assume, for the sake of argument, that he didn't attend classes (perhaps only went for exams), and that he was not registered as Obama but was registered under some other name. What, if anything, does this change in terms of avenues of inquiry?
Obama was known to some at Columbia, if you believe this May 2008 account, which may have been made up to provide some normalcy to Obama.
Personally, I think Obama has always felt like a stranger in America, which is why most of his friends in college were foreigners. He identified more with them than native born Americans. He had Pakistani roommates at Occidental and Columbia. I suspect that Obama was into drugs and radical causes. There is the very real possibility that he met Ayers at Columbia. It could be the reason why Obama headed to Chicago. No one knows why he went there.