“Why don’t fathers and children have the same last names any more?”
Many of my acquaintances over the years have had children with different last names. As to where the children came from, a common theme was, the original father and the kid’s mother met in bars and both were probably drunk. They had wild animal sex and mistook that for love. Some of them actually married and then discovered that they had nothing in common. Either one or both were alcoholics or drug users, which also tends to break up a relationship.
One of my retired friends has a 30-something son with children by a woman who became a heavy drug user. They divorced and he married a woman addicted to pain killers who had two children by somebody else. He’s trying to make this one work and I’d say he’s putting up with stuff I wouldn’t. He’s told her if she gets high again and gets arrested he’s gone.
So, in answer to your question, some of those children’s last names are due to drugs and alcohol use.
Even so, the father’s name should be on the birth certificate and the child should have the father’s last name. I understand different last name than the mother.