Power is a major theme. The Kyuubi gives Naruto immense power, and in the DxD world which is also full of powerful beings, the exploration of how this power is used and controlled is often central.
Another theme is adaptation. Naruto has to adapt to the very different rules and culture of the DxD world. He can't rely solely on his ninja skills, but has to incorporate the new knowledge of the DxD universe. For example, dealing with the different types of magic and the social hierarchies there.
One common theme is power. How Naruto harnesses the Kyuubi's power and grows stronger. Another theme is friendship, as the relationship between Naruto and the Kyuubi can be seen as an unusual form of friendship. And there's also the theme of redemption, like when the Kyuubi tries to make up for its past misdeeds.
Another theme is identity. Naruto has to figure out who he is now that he is the Kyuubi incarnate. Is he still the same Naruto? Or has this new power changed him? And how do others see him? For instance, some people might be afraid of him now that he has the power of the Kyuubi, while his friends try to support him through this change.
One main theme is friendship. Naruto forms a bond with the Kyuubi and the Nibi, which is not common in the original series. This bond is based on mutual understanding and trust.
One main theme is power and adaptation. Since Naruto is coming from his own world into the DxD universe, he has to adapt his powers and skills. And as a primordial god - like character in some of these fanfics, his new - found power is a major aspect that drives the story.
Another theme is friendship. Even though the Kyuubi starts as a somewhat hostile force, over time in fanfiction, a friendship or at least a mutual understanding can develop between Naruto and the Kyuubi. This is seen in stories where they work together to overcome challenges.
One popular 'kyuubi naruto dxd fanfic' is 'Naruto in DxD World'. It combines the unique powers of Naruto, especially the Kyuubi's power, in the DxD universe. It often has exciting battles and interesting character interactions.
One common theme is power. Since Kyuubi is a source of great power, many fanfics explore how Naruto uses or struggles with this power. Another theme is friendship. Despite their initial enmity, they can become friends in the fanfics.
Isolation is also a theme. Because of the Kyuubi, Naruto is often ostracized by the villagers when he's young. Fanfics might focus on how he copes with this isolation, whether it's by finding solace in his own training or by forging unlikely friendships despite the villagers' attitudes. This theme adds depth to the character of Naruto in the context of the young kyuubi situation.
One main theme is power. Since both Naruto and Highschool DxD have characters with different levels of power, in the fanfic, it's often about how Naruto's power compares and combines with the powers in the DxD world. Another theme is friendship. Naruto is all about friendship, and in the DxD world, there are also relationships to be formed and maintained.
Power and control. Since it involves the Kyuubi's power and a zanpakuto, a major theme is how the character controls these powerful forces. For example, Naruto has to constantly struggle with the power of the Kyuubi in the original series, and adding a zanpakuto to the mix makes it even more complex.