Im am 16 years old and the guy who got me pregnant is 19. He keeps threating to take the baby and leave, if I don't put his name on the birth certificate and give the baby MY last name will he still have his parental rights.

I wouldn't want to give him parental rights if he is threatening to take the baby away.
The only way you can do that is to not put his name on the certificate or take him to court and prove he is an unfit father.
I don't know what he can actually do (legally) if you don't put his name on the birth certificate other than to demand a paternaty test and then demand his rights once he is proven to be the father. He can not just take the baby without establishing some sort of proof. If you are afraid of him and can prove it then you can tell the Judge that you feel he is a danger. If the Judge still grants him rights then you need to request supervised visits and again you have to prove he is a danger or unstable.

As long as he really is the biological father, he has parental rights no matter what you do. The only way to take his parental rights for him to sign them away or for a court to take them away. You can give the baby whatever name you want, it doesn't make any difference as far as custody goes.

He can demand a paternity test from you and the baby if you try anything sneaky, like not put his name on the birth certificate or put a false name down.

He will not have any rights to this baby until it is determined by the courts through DNA/paternity test. If he signs the birth certificate then he has the same rights as you have until/unless you go to court and ask for custody of the child.

What is the age of consent in your state... I believe if he takes this to court and you are underage then he will be consider a sexual predator. It is very sad that a baby must be born into this situation. Where are your parents?

As the others have said... the last name you give the child has no bearing on parental rights.

As far as not putting him on the birth certificate, you would just be delaying things. If he is the father and wants rights to the child, all he has to do is request a paternity test. Upon the results, he will be added to the birth certificate.