I'm in a similar situation. I'm pregnant and the Father was/is abusive.
For your situation... if the Father is abusive, then you need to protect yourself as well as your child from him, but I would be very careful in doing so- you must make sure that he is truly abusive, not just saying angry things because you were planning on moving away with his unborn child. There's a very fine line there, that neither I, nor anyone else here really knows, except the original poster, but, OP, be very careful you don't cross that line, because it may bite you in the butt, bigtime, if you do.
That being said, this is what I learned from my situation...
If you do move to another state, do so before the baby is born. Once you're established residency in that state for 6 months, if the Father wants visitation, whatever, he must file in your residential state.
There are risks, however...
You could be court ordered to move back to the Father's state, especially if he's unable to come to your new state. You could be court ordered to provide ALL the transportation back and forth, even if it's every other weekend with the Father for two hours at a time. Also, long distance visitations tend to be longer- instead of every other weekend, for example, it may be weeks at a time, when the baby is older, to make up for the "lost time" due to distance. Also, supervised visitation may be harder to get if it's state-to-state.
As for the birth certificate...
If you're unmarried, you don't have to put the name on the birth certificate. Doesn't mean that he can't fight for paternity and have his name added in time, but until paternity is proven, you technically don't have to put his name on. Until paternity is proven and/or his name is on the birth certificate, he has no legal right to the child. In my case, my baby's father's name will not be on the birth certificate until there is a court oder to do so, because he has threatened to file for full custody at birth (physically and verbally abusive man), and if he loses, to kidnap my baby to his home country. If your believe your baby is in this kind of danger, then I strongly suggest not putting the name on the birth certificate. If you just don't want him interfering with "your" child, then perhaps you're overreacting? (Again, you know the full situation, we don't.)
I also strongly suggest getting a lawyer ASAP.