Well, Naruto might find allies among the outcasts of the new dimension. People who don't fit in with the mainstream society but have unique powers or skills. They could see Naruto as a kindred spirit and join forces with him. Also, if there are any beings in the new dimension that oppose the forces that brought Naruto there, they could be his allies. They might have their own reasons for wanting to help Naruto, like using his power to overthrow a tyrant in their dimension.
Naruto could meet alternate versions of his friends or enemies. For example, he might find a version of Sasuke who has a completely different personality or a different set of skills. This would create interesting interactions and potential conflicts or alliances.
A group of rogue ninja from the other dimension could also serve as the main antagonists. They might be jealous of Naruto's power from his original dimension and want to steal it for themselves. They could be led by a charismatic and devious leader who has a personal vendetta against Naruto for some reason, like he believes Naruto will disrupt their way of life in the dimension.
One idea could be Naruto being transported to a dimension where chakra doesn't exist, but he discovers a new form of energy and has to learn to use it from scratch. This would force him to adapt his fighting style completely.
In this type of fanfiction, a possible plot is that Naruto is sent to a dimension where time moves differently. He might age at a much faster rate, and he has to quickly master the ways of this dimension to find a way to reverse the time effect on him. Another cool plot could be that he lands in a dimension that is a mirror image of his own, but with opposite personalities for everyone. So he has to deal with a Sasuke who is overly friendly and a Kakashi who is always serious, which makes for a really strange and challenging adventure.
One possible plot twist could be that in the other dimension, Naruto finds out that all his friends have different personalities. For example, Sasuke could be a peaceful scholar instead of a brooding avenger. Another twist might be that the chakra system works completely differently in this new dimension. Maybe instead of using hand signs, they use some kind of mental power to perform jutsus. Also, Naruto could discover that the Akatsuki in this dimension are actually the good guys, fighting against an evil ninja clan that wants to take over the world.
His relationship with Sasuke would be very different. In the new dimension, Sasuke might not have the same vendetta against his brother. So Naruto wouldn't have to worry about Sasuke going off the rails. With Sakura, she could be a powerful ninja in a different way, like she might be more focused on medical ninjutsu and Naruto would see her in a new light. And his relationship with Kakashi could change too. Maybe Kakashi is a strict military - like leader in the other dimension instead of a laid - back teacher.
His relationships with others could change. If he's in a new dimension for a long time, he may form new bonds with characters there. These new relationships could influence how he views his old friends back in his original dimension. He might also learn new ways of communicating and building trust, which he can then bring back with him if he ever returns.
In reality, fictional characters aren't real in another dimension. They are just figments of our creativity, existing only in the stories we tell and the minds that conceive them. There's no scientific evidence to suggest they have a real existence elsewhere.