Birth certificate and fathers last name?

Heidi
The father and I aren't together. He wants to be involved, which I'm happy about but he is a liar and pain in the butt to deal with. I told him I want her to have my last name and he lost it and said he wouldn't sign the birth certificate. What happens if he doesn't and am I wrong for giving her my last name? What are the pros and cons of this?

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