Not putting father on birth certificate

I'm throwing around not putting the father of my baby on the birth certificate. I ended things before I found out about the pregnancy because he is a compulsive liar. He immediately got back with his ex-girlfriend. I told him about the baby out of respect of him being the father and he immediately suggested an abortion because he doesnt want a child. I told him if he felt that way, then he didn't need to be in the babies life. Since then, he has expressed interest in being in the childs life, but continually starts drama. Him and his girlfriend do nothing but slander my name at work, him and I are coworkers, and on social media. He stopped the work drama when our coworkers expressed their opinions on him being a "crappy" person, but the social media drama is a day to day battle. She has continually messaged me and does everything in her power to spread the misery she feels in her life. He cannot message or even talk to me about the baby without her permission. Since they are acting so childish, I've been throwing around the idea of giving the baby my last name and not putting him on the birth certificate. Any opinions?

No, I cannot get child support if he isnt on the birth certificate, but I can financially care for the baby without his help.