My son is 20 yrs. Old and was in a auto accident in 2006 he wants to add his fathers name th e birth certificate

Not sure he can, but he will have to go though family court. Does the father have a problem with it ?

He wouldn't be allowed to unless there was DNA to prove who the father is. Anything short of that would be hearsay because it would be impossible for him to " know " who the father is without the mothers knowlage.

No, he does not