How do yougo about  changing the name of a minor child?

Unfortunately the answer to your question is yes, to some extent.  Although your wife has never sought to establish custody or support with the boy's biological father, it does not mean that his rights do not exist.  It is unclear here if he even knows of the child's existence.  If he does and he really does want nothing to do with him it is possible that he may voluntarily agree to terminate his parental rights.  But are you going to adopt the child?  Because the courts do not like to terminate the rights of a child to support, inheritance, etc., unless there is some one waiting in the wings (and the two proceedings can be done at the same time).  Seek legal help. Good luck.