Baby Last Name


I see many women who give their baby their last name not the father's. Some say its right, some say its wrong. Im single, not married, and having a baby with a friend. We did not plan this, just happened. Wouldn't it make sense for me to give the baby MY last name? I think giving the child a father's last name who is not part of a family, and just co parenting or whatever would give him a false sense of having a "family", regardless if he will be in the child's life.