HOW do I get full primary custody if his name isn't on the birth certificate?

Really you have two options:

1.) Do nothing. Lots of people talk and talk but never go to the trouble of filling out the paperwork. If he does nothing, you effectively have the child.

2.) If he goes to court and gets a paternity test, you have to prove he is an unfit father.

See if you can document any abuse. If he makes threats, see if you can get him to leave threats on your answering machine. If he is violent, call the police and go to the ER.

If you are frightened of this person then why are you allowing him to see the child? Maybe more to do with him giving you child support and him threatening he will not pay it if he doesn't see the kid.

Name on birth cert or not matters not .......... he has no rights/responsibility until it is and the only ways to get his name on there is you registering the kid along with him ( you didn't do that) or him going to court to get a court ordered DNA test, he then has rights and responsibilities in law, the rights to see/visit the responsibility to pay child support, not married ? You need both court ordered and details set down in writing.......... and unless he can prove you are an unfit parent, on drugs, beat this kid, go out drinking every night leaving the child etc etc etc PROOF not what he thinks........ then he hasn't a cat in hells chance of getting custody

You go to court and prove that the other parent is unfit, get a lawyer.

His threats are not to be taken at all seriously. No judge is going to award him full custody unless you are declared unfit.

For better or for worse, he is also a parent.

The two of you need to act as grown people, go to court and establish paternity (DNA test), child support and custody/visitation. That way, there can be no game playing and the child's best interests will be looked after.

yes you can.

Custody has nothing to do with whose names are or are not on a birth certificate.