You should check your local courthouse for the forms. They likely have the forms you will need there. You will have to complete the forms, pay the filing fee, follow the procedure. There will be a hearing.
If Dad is in agreement, it is not going to be a complicated process. If he disagreed, you would have a difficult time.
A child having Dad's last name doesn't mean he is involved. It doesn't make him Dad. It doesn't take anything away from him either by the child having the last name of the person who is truly raising the child. That is ridiculous to pass judgment like that.