He does it because he wants control.
I don't know what happened, how long you were together, or why you broke up, but he sounds pretty unpleasant.
If you're not married, then he has no right to choose her name, you can choose whatever you like :)
I was young when I had DS. His dad wanted me (we were engaged & living together), and decided, part way through the pregnancy, that he wanted me to have an abortion. He already physically abused me, but when he did it when pregnant, I found strength, and kicked him out. He was involved in a way, but wasn't supportive.
After DS was born, he told me what names he hated. We did agree on DS's first name, but the middle one, was one I'd been 'banned' from using. As DS's dad refused to be on the birth certificate, I chose it anyway. He was trying to control me.
Have you got any RL support?
Don't make any rash decisions. It is an emotional, and scary, time. But you do have enough strength to get through this - alone if need be.
Try not to let him get to you. I do understand you wanting him, but he's just trying to provoke a reaction from you. Just try to detach from him x