Birth Certificate question

Mikayla • Vegan momma to baby Asher👶🏻💚

I won't be putting my babies father's name on the birth certificate as he is a drug addict and I don't want my son growing up around him. But I was wondering IF the father ever does clean up his act and go to rehab and I feel that he can be a good father can I then put his name on it? Or with the father part on the paper have to be blank forever?