This is an interesting question. This question is a matter of opinion and can be answered in many ways. Also answers will differ based upon what society you live. With that said, let me give you a few options about which to think.
First, you can simply ignore that person who has maligned your father. To ignore someone is to give them no recognition. It is to take their honor away, in a sense. At the same time, you can affirm your father.
Second, you can seek to defend your father's honor by setting the record straight. If there were false allegations and the maligning was public, then you can show how that person spoke falsely. In this case, you will have to publicly defend him.
Third, you can shame that person who did the maligning by living a good life with your father and letting your actions speak louder than words. In this way, you will make that person who has maligned your father look foolish for maligning a good man.