He was named as you see on the certificate. When his mother remarried Lolo Soetoro, he adopted young Barack, who then became Barry Soetoro. He later switched it back but there is no documentation for the name change.
The doctor's sig is there, by the way, under the heading of 'attendant'--field 19a. I believe the document is a forgery; just another violation of the law for the one whose story is full of holes and contradictions.
I wonder if we'll ever know the truth.

∆∆