Question Paternity acknowledgment? Bc? Name change? Custody? ?

I recently gave birth to my lil girl, her father was there through out my pregnancy even though we've never been in a relationship. He tried to get me to have an abortion for the first five months. He left me, and I took him later at about 7 months pregnant I found out he was sleeping with someone else, and talking to several other women. I remained by his side because he claimed he be loyal. When our LO was born I let him know I was hyphinating her last name. He only wanted his last name or nothing at all so I gave her my own. He didn't sign any papers. He no longer wants nothing to do with me until I make his lastname the only one and blames me for giving her my last name as the reason wr wont have a family. I care so much for him and wish things would work and us to be a family. But I'm scared of the aftermath if I do change her last name to his. I'm a first time mommy and I need the advice, please don't judge me. Thanks in advance