Baby's Last Name!!!

I dont know weather to put my so last name on the baby 
I feel like not doing it bc he has done soo much damage to me weve been together for 2 yrs now. He has cheated on me, treated me like shit, ive done soo much and tried soo hard for our relationship to work out. He is soo ungreatful for all the stuff i do and what ive done for him... and ive forgiven him soo many times.
And at this point im thinking i have to make a desicion bc our relationship is usually never on the best. Somedays he acts like a teddy bear and somedays your looking at the devil in real life soo im thinking if he one day decides to leave one day on us like he did to his daughter.... and i have his last name on my baby when i want to enroll him or her into school...
I will have to be looking for his ass and i dont want to be doing that... 
What do you guys think i should do?? 
Help me pls!!!