
Quoting
flyingron
Your reason for the change is not going to mean much to the court. Children even in intact families often don't have the same surname as the mother.
It would have been easiest to do the name change at the time paternity was established. Follow the procedures now for a minor name change. You must have either the father (the currently determined father not the ex-husband whose name is currently being used) join in the petition or you must serve him to give him the chance to object. The JDR court will determine if the change is in the best interest of the court. However, I suspect that a change to the father's name would be straight forward and a change to your name if not protested by the father would be easy as well.