One possible cause could be his sense of failure. Naruto always wants to protect his friends and village, so if he fails in a mission or is unable to save someone, it can cause him great pain.
His fighting style could become more aggressive. Without the fear of pain, he might be willing to use more extreme techniques that would otherwise be too dangerous because of the pain they cause to the user. He could push his body to the limit more often.
In many fanfictions, Naruto might use new jutsus or a deeper understanding of his own power. Maybe he taps into a more powerful form of the Nine - Tails' chakra and combines it with his Sage Mode in a unique way to overpower Pain.
One reason could be some sort of special jutsu or power - up. Maybe he got a new form or ability that suppresses pain. For example, it could be related to his Sage Mode or something new entirely.
In some fanfictions, Naruto's pain might manifest through his actions. For example, he could become withdrawn and isolate himself from his friends. This is because Naruto has always been a social person, so any deviation from his normal behavior could be a sign of his internal pain.
One popular 'Naruto is Pain' fanfiction could be 'The Transformation of Naruto into Pain'. It might explore how Naruto, through some unique circumstances, begins to adopt Pain's ideology or power. Another could be 'Naruto: Pain's Legacy' where Naruto has to deal with the after - effects of Pain's actions in a very personal way.
It could be about Naruto having some sort of connection to Pain. Maybe in this fanfiction, Naruto is somehow related to Pain in a way that wasn't in the original story, like being his son in an alternate universe. This could lead to a whole new set of storylines, with Naruto perhaps having to deal with the legacy of Pain while also following his own path as a ninja.
Konan could be really interesting. In some fanfictions, she might have a different backstory or motivation that affects the Naruto vs Pain fight. For example, she could be secretly trying to stop Pain from going too far in his destruction of the Leaf Village.
Jiraiya could be a great addition. Since he was Pain's teacher, his presence could add a lot of depth to the story. He could offer insights into Pain's past and also help Naruto understand Pain better.
Another reason is that fans are always curious to see alternate storylines for their favorite characters. With Pain, there are so many possibilities. Writers can create scenarios where Pain teams up with Naruto earlier, or where he has a different view on the Hidden Leaf Village. This allows for a great deal of creativity and variety in the fanfiction.