How come Naruto has is mom's last name and not his dad's?



Well to your first question,ya most of the time the child,usally takes the fathers name,but obivously not in this case. The reason is because Narutos father didn't want anyone knowing that he had a son. He didn't want to let is enemys know that he had a family,because if they were to find out it could work against him and be is weakness,as they were target his family. This was done for Naruto's own protection.