Giving baby by last name?

About to go through divorce. Dads a deadbeat. Hasn’t helped at all with getting anything for the baby bc in his eyes “she’s not here yet” even though I’m due in a week. He’s says I’ll pay child support when she’s born. Even though it’s necessary to be prepared with everything she needs now, so I been doing it all alone. He’s in a different state bc he chose to and there’s a 50/50 he will even make it to her birth. 😒 He also doesn’t have money for his ticket yet) which he’s had 5 months to save for and was working.. so doesn’t make sense to me. At this point I want full custody. He wont be around much due to him being far and his job. He’s emotionally cheated on me while pregnant (nudes, sexting, multiple girls, plus didn’t care he did it) and was back and forth about wanting to be a family. This pregnancy was stressful with him not knowing what he wants. Love bombing me and then changing his mind.. Baby is almost due and I have been considering giving her my last name because once divorce is done I will be changing mine back too. I want full custody because he’s irresponsible, will never be here for her, had DV abuse in the past, and lives with his manipulative mom. She’s toxic and even told me it’s my fault for him wanting to get with other girls. I AM PREGNANT. Who says that?! I really don’t want my baby with them. I would love to move on without needing to coparent with someone like him. I feel the court would allow me full custody based on his history. Not sure how it works if parents are in different states.

Thoughts if baby should have my last name ? I am too carrying even when he’s treated me so bad these past 9 months.. That’s why I’m asking for advice.

Thanks for your responses.