The significance of this is that Barry was using his Indonesian name, and of course, his Indonesian passport.
The Occidental website, in reporting the news of Soetoro being elected president, stated: "It was at Occidental where he stopped being called `Barry' and became Barack Obama, Newsweek pointed out in its account of Obama’s formative years that featured his black-and-white freshman photo on the cover."
Two other friends from Occidental, Tom Moyes and Ken Sulzer, remember him as Barry. Sulzer, when he first realized it was Obama, called Moyes to state: "That’s Barry, man,’” says Sulzer, mistakenly thinking Barry was simply a nickname Obama went by during his youth. It was no mistake apparently because he was Barry Soetoro at the time named after his step-father.
His mother and adopted dad got divorced in August of 1980. As he entered Occidental in 1979 he used his Indonesian name, and most likely his Indonesian citizenship and passport, then immediately after his mom's divorce he desired to revert back to his birth name of Barack Obama.