He might react with hostility. Dark Naruto has a certain edge to him, and if he sees Rias as a threat or someone he doesn't like, he'll likely oppose her. He could use his combat skills to challenge her directly.
In some fanfictions, Naruto can be made into Rias' boyfriend through creative writing. Fanfiction allows for crossovers between different fictional universes, and writers can imagine unique relationships. However, in the original Naruto and High School DxD (where Rias is from) storylines, there is no such relationship.
In some cases, it could be that the author of the fanfiction simply wants to explore a different narrative where Rias is not the 'perfect' character she is often portrayed as in the main series. They might want to create a more complex or alternative view of the Naruto DxD universe by highlighting what they see as flaws in Rias's character.
If Naruto was Rias' boyfriend in fanfiction, there would be a huge cultural clash at first. Naruto comes from a world of ninjas and honor, while Rias is in a world full of demons and magic. But as they get closer, Naruto could teach Rias about loyalty and never giving up. And Rias could introduce Naruto to the more complex social and magical aspects of her world. Their relationship could also change the power dynamics in the High School DxD world as Naruto is extremely powerful in his own right.
A common theme could also be her role as a leader. Fanfiction authors might write about her being a bad leader, making wrong decisions that lead to negative consequences for her group. This could be a way for the author to explore different leadership styles and show how things could go wrong under Rias's leadership.
One possible idea for this fanfiction could be Naruto being transported to the world of High School DxD. He might end up attending the same school as Rias. Given Naruto's strong sense of justice and his combat skills, he could quickly become involved in the supernatural battles and power struggles in that world. He might also form an interesting relationship with Rias, perhaps starting as friends and gradually developing into something more as they face various challenges together.
In fanfiction, such a betrayal could occur due to power struggles. Maybe Rias sees Naruto as a threat to her position in the Highschool DxD world. She might fear his growing power and influence, which could overshadow her own. So, in order to maintain her status, she betrays him.
Naruto could bring a lot of energy and a new fighting style. His ninja skills would be a unique addition. For example, his shadow clone jutsu could be used for various strategic purposes in battles against other peerages. His positive and determined attitude would also be contagious, inspiring Rias' other servants to be more bold and confident.
Naruto, being the open - minded and adventurous type, would likely find it fun to read fanfiction about himself. He could be amused by the creative ideas, even if some are a bit far - fetched. He might even take some of the positive ideas and think about applying them in his real adventures. Rias, however, would approach it more skeptically. As a devil princess, she has a reputation to uphold. She would carefully analyze how the fanfiction portrays her, and if it goes against her values or the image she wants to project, she might be a bit offended. But if there are some good aspects, like new ways of handling her devil powers or relationships, she might consider them.