This can depend on your state laws. You may be only allowed to give your LO's your legal last name if you are not married to the father of the LO.
SOME states you can give your baby any last name you want even if you made it up.
You will want to look up your state's laws.
But really don't over think this one. Your baby is your baby and it doesn't matter what last name you all have.
My dd has my maiden name, my ds has my 1st married name/last name of their father and I now have my Forever Husband's last name. We have 3 different last names and my kids are full blood siblings. It was just how it worked out and I've never had a problem claiming my children. Sometimes I get Mrs. wronglast name but matches the child we are talking about. That is a quick correction and move on.