step parent adoption/no bio-Dad recorded

What is the name of your state? Ohio

I had a daughter when I was 17 to a guy who physically abused me.By the time I found out I was pregnant,we had broken up quite bitterly.When my daughter was born,I did NOT list anything under 'Father's Name' on her birth certificate.Now my daughter is 9 and I have been with my husband for 5 years (married 2 years).He wants to adopt my daughter.My question is: since I did not list a father on her birth certificate,does that exempt us from having to deal with trying to find him to get his consent for the adoption?He's never even seen his daughter and would probably make things VERY ugly if we tried to involve him.I also would not want him to have any sort of access to her,given his past drug history and physical abuse of me.I did make the mistake of giving her his last name,which she no longer wants to use (she wants to use my husbands last name,which is what her brother has).Could she use our new last name at school while the adoption is pending?Thanks for any advice.