Another possibility:
obama was either obama at birth, or perhaps on the vault certificate Dunham, since obama senior was already married. The original birth doc could have listed father: unknown and race as white.
Adopted by Soetero and used Soetero’s last name so the birth registration from obama or Dunham would reflect a legal name change. The original would have been sealed and new document issued to change his name to Soetero.
When he chose to use obama, signifying another legal name change, the birth document would have to be changed again, Soetero sealed, and obama reissued, or perhaps issued for the first time since it might have been Dunham originally.
That is the doc we are seeing now. It would be the third COLB on file, but two previous would be sealed.
There could be three or four certificates with names on them: if Barry was brought to Hawaii shortly after being born in perhaps Canada, the name might have been Barry Dunham; when supposedly Obama and Satnley Ann married, the name might have been changed with an Obama adoption to Barack Obama; when Lolo married Stanley Ann and adopted Barack, the name might have been changed to Barry Soetoro; when Stanley Ann came back to Hawaii and divorced Lolo, she may have had Barry’s name changed back to Obama. But it is more likely that a name other than Obama was on the first filing. The Pres_ _ent’s actual legal name may still be Barry Soetoro and allowed him to game the systems of passports and college entry and financial assistance through that name. Only when he decided to ‘embrace his blackness’ when heading to New York to Columbia did he switch to using Barack Obama, perhaps, always ‘perhaps’.