Adopted...Is it possible he was adopted by his mother.
I think it is FAR more likely he was adopted in Indonesia by his step-father, Lolo Soetoro:
... and retained his adopted name (Barry Soetoro) when his mother, Ann Dunham, dumped Barry/Obama Jr on her parents back in Hawaii in December 1971 -- Ann Dunham remained with her daughter in Indonesia. Obama assumed his "nickname" of Barry Obama in the Hawaiian school system.
Barry Soetoro/Obama Jr came to the mainland when he graduated high school in Hawaii in 1979, probably under the name Barry Soetoro. Occidental is a private college and is not subject to "Freedom of Information Act" requests -- which is why there are lawsuits to see those records. Obama was able to "un-establish" his adopted name, Barry Soetoro, through divorce papers and other legal documents during or after the proceedings began in the August 1980 Soetoro divorce.
BUT ... Obama's time of reckoning will soon be here. And we know he won't go quietly -- at least not without Michelle taking the linens and silverware first.