Can I add my last name to my 6 year old if I never was married to the father?

Please clarify your question. Did you give the child the father's last name? If so, why are you trying to change it?

You give a child their name when the birth certificate is completed and filed. If you want to change the name, either completely or by adding a hyphenated second surname, this requires a court order. Both legal parents usually will need to agree to the change.

Any question on law needs to include your general local as laws vary by area.