How do I go about changing my sons last name? His father and I are now married and he wants our last name now. My other son also wants his fathers last name whom is now deseased. How can I avoid many legal costs to have this done?

You can file with your local court. Court fees may apply or if your at the poverty level they may be waived. You will need copies of the birth certificate and also your ex's death certificate to take to court with you. Then you can fill out the forms and explain to the courts why this should be done and that all related parties are in agreement. Also when you submit certificates to the court I would recommend getting certified copies so it has the stamp of approval on it before the judge sees it. That way its less likely to be questioned.