Should the baby have the fathers last name?

Need opinions on giving your child their fathers last name if you and the father aren’t together & he isn’t helping out with any of the bills during the pregnancy. This guy begged and cried to be with me for months,but as soon as he got me pregnant he broke up with me to avoid responsibility. I already have one baby, he’s 11 months old, he has my last name and his dad isn’t even in the picture now. He wasn’t there during the pregnancy either that’s why I didn’t give my son his last name. And now I’m glad I didn’t! The only difference is this guys family is wanting to be around and help me out. I’m just torn on the last name.