it depends what state you live in they have different laws. In Indiana you could name him after the dad but wouldn't have his last name if hes not there to sign the birth certificate. So it really depends
You can put him down as the father and he can always go back and sign it later. It doesn't effect the name though
Oh okay I thought for a baby to be a Jr the dad had to sign the birth certificate
I don't understand, you mean the name? You can name baby anything you want no matter the dads situation :)