Do I understand correctly that you mean nicknames of two persons of whom one is called Unwise and the other - Sage?
I don't see any reason for not calling them antonyms. One would have to think that proper names can't have any appellative part of their meanings to say they are not antonyms. And that would be - in my opinion - hard to defend.
I'm not saying it's always this way. Many proper names have little or none appellative function. Your examples show it very well. But when I go to Very Dark Wood I can think I'd better take a torch.With most proper nouns, the original meaning is associated more with the derivation. If you meet a woman called 'Faith', is religion the first thing that leaps into your mind? There are cases (North/South) where a case can be made out for antonyms, but with people and place names, I think it would be strained and artificial to do so- a proper noun denotes the person/thing etc more than the etymology.
Is atheism or really the antonym of someone called Faith? And what's the antonym of London? New York contrasts with York, but that's not an antonym, or even much of a association to many- when I hear the words, I never think of York.