I as adopted at the age of seven, I carry my Dad's name and he is shown on my birth certificate. The information about includes where he was living, working, race, etc.
The original BC of Obama is locked and has been replaced with a new BC that establishes parentage, race and personage.
If Barry was adopted by Lolo, we would need to establish when Barry came back to the US, Under what passport and visa, when he changed his last name back to Obama(I have looked into this and it is a very arduous process. However, you can NEVER change the information on your birth certificate, ever).
We would need to know if he is still a foreign national or when that status ended and what the process was for that. What were the supporting documents to establish USA citizenship, etc.
You *can* amend your birth record so the COLB printout will be changed. The underyling “birth certificate” is there is one would not itself be “changed” necessarily. The amendments would be added to the record, but the original information would still be there.