I suspect the deal is that husband number two...the Indonesian dude....adopted Obama...renaming him as they left the country. This is this “funny” business that he really can’t come up and announce that he’s got some Indonesian name because it then demands an accounting over his citizenship (if his new dad conferred Indonesian citizenship on him....it really invites too many questions to answer today). I think this is the entire problem. The funny thing is that someone in Indonesia is going to let the cat out of the bag sooner or later, then congress will have to step in to fix something impossible to settle easily.
He was registered in his school in Indonesia as an Indonesian citizen. From what I can determine, a child who was a citizen of another country but had an American parent (and thus potentially had dual nationality, if it was one of the countries with which the US had this agreement at the time), would have to declare this when he was 18 and renounce the other citizenship. He doesn’t ever appear to have done so, and there’s some suggestion that he travelled on an Indonesian passport when he went to Pakistan in the 1980s. It’s complex, the law has changed several times since then, and I don’t know if it’s really worth looking into.