Ah, a whole different topic… my niece’s mom did that. My brother fought this, and ultimately a version was issued with his name on it. The mom continued to use the one without his name, until he died unexpectedly and she wanted to collect social security for my niece. Then the mom scrambled down to the courthouse to get a copy with his name on it (she had disposed of the copy she originally received, I think). Not sure how this would work if you tried to add the name after his death – but there could be financial advantages in life to having dad’s name on the birth certificate, too.