Please help, 💔.

Okay so a little back ground first.
Me and my boyfriend have been together for quite some time now and we are expecting our first child together.
He has done some things that weren't great in our relationship, but I've tried to push that away and make our family work.
But.... The times we have argued he always says stuff like "if we break up, I'll take away the baby from you" stating that he'll be raising the baby and I'll just be "visiting" that really breaks my heart.... And sometimes leaves me confused on how to handle this.
So now, the help I need has to do with birth certificate etc. 
I don't know much about these things since this is my first child and I never imagined getting told these things. 
What is the purpose of a father being on the birth certificate? Should his name be on it?
Does that make it easier for him to take my baby away?
What are other things I can do to make sure that if we ever do not work out my child will still be with me?
I feel like I'm a perfect fit person who can be a mother, I have a wealthy family and supportive family, I'm going to college, i have a future for myself and my child; and he makes me feel like it'll be so easy to take away my baby.
Please help.
#Texas