Look if the police and social services have told you to leave his name off the birth certificate take their advice, they have vast experience of how the darker elements of human society operate, unlike most of the perfectly reasonable, pleasant people on here.
The police especially are the poor sods who attend the crime scene 1st when it all goes wrong, and have to call the ambulance all too often, advice like this from them is NOT to be taken lightly as most experienced officers have had to see things which would make our hair turn white. They see humanity at it's best and worst sadly.
Also remember IF social services deem you to be putting your child at risk by ignoring their sensible advice (based on their experience of the MO of dangerous men, which sadly will be greater than your own) then you put your OWN rights to contact & parental responsibility with the child at risk. This is the worst case scenario but it's the truth.
In cold terms - ignore their advice and they can and will take the child away from you too, in order to protect that child if need be. Seriously if your gut instinct and the police, and social services professional all think the man is a risk to the child it's really unlikey that you are ALL wrong is it?
At that point those same people who tutted at you for refusing to give "Dear Daddy" PR via his name on the birth certificate will "tut" at you some more. If he has you so scared you've already felt the need to move house and uproot your existing children ignore all the "fathers rights" brigade and take my earlier advice.
If he is a perfectly reasonable human being who is freaking at the thought of losing the flesh and blood he wishes to raise and protect with love and kindness he'll be willing to swallow his frustrations and agree to whatever conditions a court applies to him in order to see his kid. You'll know by the time the kid is a year old if he's made the effort to respectfully apply to a court for PR, humiliate himself through supervised contact at a centre and apologised (via a letter) for scaring you out of your home. His name can be added to the birth cert in a decades time if you deem it appropriate - that's not a priority today, keeping yourself and new bubba safe is.
What normal parent wouldn't be willing to go the extra mile for their kid? ALL decent parents will swallow their pride and walk over hot coals if need be to see their children. If this is just a temporary freak out on his part, then time will make that clear, and you'll be able to adjust your approach to him accordingly. On the other hand a newborn is waaaay too vulnerable to allow anywhere near someone who scares you out of your own home when pregnant and that the police & SS deem to be a risk.