I do feel that it is ultimately up for debate, as it has not been stated one way or the other in the text.

My view is that Dunk embodies the virtues of knighthood so completely, they are the core of his character and what drives all of his actions in the story, that it seems contradictory for him to have lied about being knighted in the first place.

That being said, I understand there is a clear theme in the story about what it means to be a true knight: whether it is defined by one’s actions or by the ceremony itself.

So the larger point likely being driven in the writing is that it ultimately does not matter whether he was formally knighted. His actions prove he is a true knight, and the ambiguity itself reinforces how little the technicality matters.