Register the baby alone, then the father can't go on the bC.
Register YOUR surname. It gives your baby a connection to you. The one that IS there for him/her.
I was with my ex when DS was born/registered. We're not together anymore, and Ex is now abroad and has been so for 3 years. He was abusive to me, so contact is purely due to DS.
I did register ds with Ex name. I kind of wish I didn't, but apparently inheritance in Ex country is impossible if a western name/name different to the father is used.
At school though he's now only known as .
When I registered him for infant school I used his official name as I had to, but stated a 'known as' name. When he went from one school to the next, I didn't bother with the official name, so he only has MY name.
This gives him the right in the future to choose. He could get passports etc in my name if he can prove a link to it, which he can,
In your situation love, (and actually in ALL unmarried cases) i'd strongly recommend that the mother's name is used. No unmarried partner has the right to complain imho, as if they marry you, the bC etc and name can be automatically changed.
Give your child the link to you, not to someone who looks set to only ever disappoint you/them.
It's bad enough realising that the living being that you most love in all the world has a woefully idiotic father, but don't further rub it into your own wounds by bestowing the honour of furthering his lineage when he's done nothing to support either of you.