Well, it could be due to his appearance. Maybe he was wearing something similar to Hawkmoth's style by accident. Or perhaps his actions were misinterpreted. He might have been in the wrong place at the wrong time, like near a recent Hawkmoth attack site looking suspicious.
In the fanfic, it could be that someone with a vendetta against Hawkmoth saw Adrien and jumped to conclusions. Maybe Adrien has a similar build or gait as Hawkmoth. Also, there could be false rumors going around that led people to suspect him. For example, if there was a leaked, blurry photo that made Adrien look like Hawkmoth from a distance.
It could start with a misunderstanding of his family connections. Maybe his father's business dealings or some secretive family affairs made people think he was involved with Hawkmoth. Also, Adrien might have some new powers or abilities that are not fully understood and they seem similar to what people believe Hawkmoth has. And there could be a character who is out to frame him, spreading lies that he is Hawkmoth.
He'd probably face a lot of hostility. People might avoid him or even try to attack him.
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.
It might be that a trusted ally shares some vital information with Adrien, allowing him to piece together the mystery of Hawkmoth's identity.
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 through some clues and his own detective work. He could have pieced things together after observing certain patterns or actions.
Well, Hawkmoth might become more powerful. Maybe the villain guide teaches him new ways to manipulate people or use his powers more effectively.
Maybe the joke is 'Why is Hawkmoth always so stressed? Because he has too many akumas to manage!'.
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.
One possible reason could be that Marinette has been acting strangely in ways that seem to Adrien to be related to Hawkmoth. Maybe she has been seen in places or at times that are suspicious, like near akuma attacks or where Hawkmoth might be operating from. Another reason could be that someone has been spreading false rumors about Marinette, leading Adrien to believe she has some connection to Hawkmoth.
One possible reason could be that Adrien is being blackmailed by Hawkmoth. Maybe Hawkmoth has some information or has threatened someone Adrien cares about deeply, like his friends or family. So, in order to protect them, he decides to help Hawkmoth, even though he knows it's wrong.