Maybe through some clues and his own detective work. He could have pieced things together after observing certain patterns or actions.
It might be that a trusted ally shares some vital information with Adrien, allowing him to piece together the mystery of Hawkmoth's identity.
It's possible that a trusted ally shares vital information with Adrien, enabling him to unmask Hawkmoth. Or, maybe he catches Hawkmoth in the act during a critical moment.
Maybe through a secret clue or a special event that reveals her identity.
In some fanfictions, it might be through a sudden reveal or a series of clues that lead him to the truth.
If Adrien were Hawkmoth in fanfic, it could change the dynamics of the story completely. It might explore his internal conflicts and the impact on his relationships with other characters.
Maybe Adrien noticed some strange behavior from Nino that seemed similar to what he imagined Hawkmoth would do in fanfiction.
Perhaps Adrien becomes Hawkmoth because he's been pushed to the edge by Ladybug's rejections. As Chat Noir, he's constantly in love with her but feels unappreciated. The pain of this unrequited love could twist his perception of good and evil. He might think that if he were in control as Hawkmoth, he could make Ladybug see him in a different light. He could use the power to create situations where Ladybug has to rely on him more, or at least understand his pain.
Maybe his dad gives a small smile and a nod. He could be a bit reserved in his reactions but still show that he appreciates Adrien's attempt at humor. He might say something like 'That was quite clever, Adrien.'
It could lead to all sorts of interesting plot twists. Maybe Adrien has his own reasons for helping Hawkmoth, or it could be a case of being misled.
Sometimes, it could be through a magical reveal or a series of clues that he pieces together.