Single mom, birth certificate ,last name

My boyfriend has kicked me and my unborn baby out of his house and clearly broke up with me. He is 40 yrs old, I am 23 and 5.5 months pregnant. I am now living with my mom and step dad. Temporarily I hope. Were only 4 miles away from him which makes it hard. However, I've decided my baby will have my last name. What I'm not sure of is, whether to put him on my babies birth certificate or if I should have him there when I have her. The reason I am unsure is because he doesn't show his care for either of us. He has hit me since being pregnant, two times. Once hit once choked and thrown around, risking her life n my health. He is around all sorts of irresponsible people and dangerous/inappropriate things. He has another son who is almost a teen but since we have had him he hasn't watched him, whenever he can pawn him off he does. He wouldn't take me for custody of her becuz he doesn't want the responsibility. He never wanted children, but said he wanted a daddy's little girl 2.5 yrs ago when we got together, which he'd now be getting. But the people and things he's around make me nervous to put him on it and give him any kind of rights to her. And if he's around when she's born I'm afraid hell flip if he sees I don't put it on or hell put it on himself, not to mention he got rid of us, is it fair for him to ditch til it's convenient and time for her to come, then him get the same experience that I did everything n waited for? If I put it on I can get support (he makes plenty a week to help provide for her) but then he has rights to her and take her around all these crappy people and ways of life, but if I don't there is no risk of her being around them, but I can't get any help. Which at first I didn't want but now I'm not sure. Please help me.