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.
First, keep in mind the context in which we're debating this issue - the question being discussed is "Was Obama adopted in Indonesia, and if so, why doesn't his HI birth certificate that was released, reflect that adoption"
In that context, it doesn't matter if Obama's father did or did not know about his own son's birth, ever really. All that matters is how Hawaiian law viewed Barack Obama as Jr's legal parent. If they were married in the eyes of the HI law, which seems clear that they were, and Sr's name is on the birth certificate, and clearly it was, then Stanly Ann Dunham would have had to sue to terminate her ex-husband's parental rights before a step-parent adoption could have been recognized by HI law - which would then have allowed a HI judge to issue a court order to amend the birth certificate.
There is absolutely no evidence any of that happened.
And, BTW, even if ALL of that did happen, it would have had absolutely no impact on Obama's citizenship status as he CLEARLY returned to the US WELL before attaining the age of majority, which by any account would have FULLY preserved his US citizenship.