I have a question, child is 13 years old, father is not aware he exists, was not named on birth certificate. Mother has been married to someone for 9 years who has been in the child's live since the child was 2 months old. That male would like to have the child take his last name, as all the family has one name and the boy has a different name. Mother never obtained or applied for sole custody of the child. What would they have to do to have his named changed?

First its not a good idea to piggyback your question on another thread. This can lead to confusion. So I've moved your question to its own thread.

Go to court, preferably to file for adotion. The court will require that they try to contact the bio father to get his permission either for the name change or adoption.

You may do a name change, but paternity will need to be established and the bio father has to sign to agree.

For adoption, the bio father is contacted and signs over his rights and agrees to allow the adoption.

This often works better when there is a child support order in place and child support ends.
If the bio father was never told about the child, I expect this may become a larger issue