Birth certificate question:

I don't really want to get into the reason why and I don't really need your opinion on the matter, just know the father of my child doesn't always make the best choices and as a parent, it's my job to keep my child safe at all times. That being said, I have NO intentions of keeping her from him and more than anything want him to be involved in her life, just on my terms (as does he want to be involved also) 
So my question is:
Can I give her his last name but NOT put him on the birth certificate. What complications could arise from this? Can he fight to be put on the birth certificate? 
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My intentions are to one day, when he starts making better decisions, to put him on the birth certificate. But until then, I have concerns and want to do what I can to make sure she's safe.