Obama is married to Dunham and his name his on the birth certificate, and as such, he was the natural legal father.
Granted that. But that is only his name. Not his signature. And he denied his supposed son in at least formal documents between 1961 and 1963. And with the formal divorce filing 1964 - the records have been ‘cleaned up’. Not recently probably in 1964. If his name was not on the initial record it was after that divorce. That divorce is the anchor and the scorched earth to everything prior. As it was done in the 1960s.
But did Obama even KNOW he had a son? Or did he ever acknowledge it for doubts before 1964? Other than old hippie governor there is no collaborating evidence - formally or informally that Obama Senior ever acknowledged his namesake until April 1964.