It could be through a series of clues and investigations that lead him to the truth.
Adrien might figure it out by piecing together various mysterious events and observing Hawkmoth's actions closely. It could also be that he has a moment of realization when something unexpected happens that connects all the dots for him.
Maybe through some clues and his own detective work. He could have pieced things together after observing certain patterns or actions.
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.
It might be that a trusted ally shares some vital information with Adrien, allowing him to piece together the mystery of Hawkmoth's identity.
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.
He'd probably face a lot of hostility. People might avoid him or even try to attack him.
Maybe the joke is 'Why is Hawkmoth always so stressed? Because he has too many akumas to manage!'.
One implication could be that it might strain their friendship a bit. If Adrien really believes this in the context of fanfiction, he might start to act differently around Nino.
One common theme is self - discovery. Adrien often discovers new aspects of his powers or his own strength during the fight with Hawkmoth.
If Adrien becomes Hawkmoth in fanfiction, Paris would be in for a major shock. His friends, like Nino and Alya, would never suspect him at first. And Marinette, who is Ladybug, would be facing a completely different kind of enemy. She's used to fighting Hawkmoth as this unknown figure, but now it's someone she knows so well. It would change the dynamic of their battles entirely.
Maybe Adrien noticed some strange behavior from Nino that seemed similar to what he imagined Hawkmoth would do in fanfiction.