I agree with my colleague's response but would add, based on your adoption flag, that
If your husband wants to adopt, and your son wants to be adopted, then you will need an attorney's assistance to file termination of paternal rights based on abandonment, and then the adoption.
This answer is general information which does not establish any attorney-client relationship between the person asking a question and the person answering, or a duty to respond to ongoing questions; nor is it intended to replace competent legal assistance in the jurisdiction where the matter/issue arises or is before a Court.
You may petition to name change. You will need father permission OR an order of abandonment. Thus, notice to the father is required.
Hire counsel. If this can be done, it will take a couple or three months time.
You can file a petition for name change and serve the father. He can then agree to the change and sign the order or more likely he will fail to appear in court and judge will grant the name change. You can also do a termination/adoption and request a name change.