Baby daddy problems

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Ok so the day I found out I was pregnant my (now ex) bf went through my phone saw the test before I had a chance to tell him and left because I didn’t tell him he thought I didn’t know whose it was. Now that was dumb of him cuz we lived together and I’m very loyal but whatever were broken up and I don’t care about him anymore. He insists that my pregnancy is fake even though I have peed on a stick in front of him and it showed pregnant. He thought it was a fake test. (Lol) so now he says he won’t believe me till he buys the test and I pee on it in front of him. Now this has been reached so far that frankly he’s just not gonna be in my life anymore. I have photo and video evidence he’s abusive physically and emotionally so I know I can show a judge he’s unfit to be a father. But now I’m thinking and I can’t shake off him not being in this pregnancy with me. Like I’m gonna be alone and single and no one wants a single pregnant woman so I just have to remember that I have a lil peanut growing in me to keep me company. Do you think I’m being irritational if I dont include him in naming the baby and labor? I frankly don’t want his input on this baby since he doesn’t seem to care at all about it. But then I think maybe he’ll change ? I just don’t know what to think