Well, he might use his ninja skills to become a hero in that world. He could teach the locals about chakra and how to fight like a shinobi. Maybe he'd make new friends and form a team to face the challenges there.
His character could become more adaptable. Having to deal with a whole new world, he'd learn to be flexible. He might also become more empathetic as he meets different kinds of people with different problems.
In some 'harry gets summoned to another world fanfiction', a cool plot is that Harry gets summoned to a world where magic is scarce. He has to figure out how to use his existing magic knowledge to help the people there discover or regain their magical abilities. Or perhaps he's summoned to a world where there are mythical creatures he's never seen before, like giant talking birds or shape - shifting foxes, and he has to form alliances with them to survive.
Maybe there are noble knights in the new world who recognize Naruto's courage and strength. They could form an alliance with him, with Naruto teaching them some stealth and speed techniques from his ninja training, and in return, the knights could offer him protection and knowledge about the new world's politics and social structures. Another potential ally could be a group of outcasts or rebels in the new world. They might be fighting against an unjust regime, and Naruto, with his sense of justice, would naturally side with them. Together, they could plan strategies to overthrow the oppressors, using Naruto's unique skills and the rebels' knowledge of the local terrain and the weaknesses of the regime.
Hermione might be a common character. Since she's Harry's friend and very intelligent, she could be summoned along with Harry or find a way to follow him. Dumbledore could also make an appearance in some stories. He's very powerful and wise, so he might show up to guide Harry in the new world. Ron could be another one. His loyalty to Harry might lead him to try to rescue Harry from the other world.
One interesting plot could be Naruto having to deal with a completely different chakra system in the new world. Maybe the chakra there is more wild and uncontrollable, forcing him to adapt his jutsu usage.
He might be really confused at first. Naruto is from a world of ninjas and chakra, while the Potterverse has magic wands and spells. He could try to use his ninja skills there and end up causing chaos as people don't understand what he's doing.
Naruto adapts to the new world through a series of steps. Initially, his natural curiosity drives him to explore the new environment. He is not one to shy away from new things, so he actively seeks out knowledge about the new world. His experience in facing difficult situations in his own world gives him the confidence to face challenges in this new place. He may face some setbacks, like not being able to communicate effectively at first, but he perseveres. He also uses his ninjutsu in different ways, for example, if there are magical elements in the new world, he tries to combine his chakra - based techniques with them. Moreover, his ability to empathize with others, which he developed in his own world, helps him build relationships in the new world, which is crucial for his adaptation.
It could be a giant eagle - like creature. Eagles are often associated with freedom and power in many mythologies. Naruto could summon it to gain an aerial advantage in battles, allowing him to quickly move across the battlefield or scout areas from above.
Yes, the main characters of novels like "Beast God of the Mystic World","I became the fiercest Summoned Beast","I'm actually a Summoned Beast","I became a Summoned Beast", and so on were all summoned into Summoned Beasts, mutated beasts, or other strange forms to the Otherworld.