Perhaps in this different dimension, female Naruto is a princess. But she still has her ninja spirit. She uses her skills in a different way, like using her agility to outwit court conspirators. And she might even start training the palace guards in her ninja ways secretly.
He might face different types of chakra and powers that he's not used to. In a new dimension, the laws of nature regarding ninjutsu could be completely different. For example, his Shadow Clone Jutsu might not work as effectively if the chakra in that dimension behaves in an unexpected way. Also, he could encounter new and strange creatures that have abilities he has never seen before, making it difficult for him to fight or even communicate with them.
In fanfiction, if Naruto is sent to a different dimension, he might face all kinds of strange new powers and enemies. For example, he could encounter magic that is completely different from chakra. He would have to quickly adapt to survive. Maybe he'd find allies who are also lost in this new dimension and together they'd try to find a way back home while also dealing with the local threats.
A possible plot is that female Naruto enters a dimension full of mythical creatures. She has to befriend some of them to learn about this new world and find a way to return to her own. For example, befriending a dragon that can help her fly over the strange terrains.
A new type of sage could be introduced, maybe from a dimension where sages have different powers and appearances. Or a group of shadowy assassins from a dimension that specializes in stealth and assassination techniques far beyond what Konoha has seen. Another character could be a talking tailed beast from a dimension where they have more sentience and can communicate freely with humans.
One idea could be Naruto getting trapped in a dimension where chakra doesn't exist, and he has to learn new forms of power. Another could be a dimension where the Akatsuki are the heroes, and Naruto has to figure out how to co - exist or change that world. Or perhaps a dimension where all the dead characters are alive again, but in different roles, like Itachi as a rogue ninja fighting against Konoha.
Naruto might start by observing. He would watch how things work in the new dimension. For example, if there are new forms of energy, he'd study how people use it. Then he'd try to apply his ninja skills in new ways. Like if there are flying creatures, he could use his shadow clone jutsu to distract them while he figures out a way to either befriend or defeat them.
Well, he could expect adventures that test his limits. Maybe in this different dimension, there are no villages and ninjas are more like lone wolves. Naruto would have to learn to survive in this new environment where the rules are different. He might also find that his reputation as a hero in his own world means nothing here, and he has to prove himself all over again. This could lead to him having to fight for respect and to make new friends. And of course, there could be new and strange creatures that he has to either fight or befriend.
The main difference might be in the settings and storylines. 'Me in comics' could focus on a more traditional comic environment, while 'dimension me' might involve alternate realities or fantastical elements.
Naruto's positive and determined personality will drive him to keep exploring the new dimension. His never - give - up attitude means he won't be easily discouraged by the initial difficulties. For example, if he encounters a powerful foe, he'll keep trying to find a way to defeat it rather than running away.