One consequence could be that he faces opposition from some clan members who might not be ready to accept him as the leader right away. After all, taking over a clan is a big deal.
Another potential consequence is that Naruto's relationships with his friends and the village could change. He now has a new set of responsibilities towards the Uzumaki clan. This could lead to some conflicts of interest. For instance, if the village's needs clash with the needs of the Uzumaki clan, Naruto would be in a difficult position. He would have to find a balance between his loyalty to the village and his new role as the leader of the Uzumaki clan. Also, his time would be divided between his usual ninja duties and the clan - related matters, which could be a big adjustment for him.
Maybe Naruto proves himself worthy by showing off his powerful jutsu skills that are related to the Uzumaki heritage. He could also use his status as a hero in the village. By winning the trust and respect of the Uzumaki clan members, he gradually takes over the leadership of the clan.
One major consequence would be in terms of his abilities. Kushina was known for her powerful sealing techniques. So if Naruto becomes her, he might lose some of his unique Naruto - like skills and instead gain more proficiency in sealing. This could change the way he battles. For example, he might rely more on sealing away enemies rather than his usual Rasengan and Shadow Clone techniques. And his role in the village as a protector might also change as he adapts to Kushina's abilities.
One possible consequence could be that Naruto grows up away from the influence of Konoha's shinobi culture. He might develop a different set of values and skills. For example, without the guidance of Iruka and Kakashi, his understanding of ninjutsu and teamwork could be very different. Also, his relationships with characters like Sasuke and Sakura would be greatly affected. Maybe he wouldn't have the same rivalry with Sasuke, and his bond with Sakura might not even form.
His friends from Konoha like Sakura and Shikamaru might support him. Sakura could offer her medical skills to help any ailing Uzumaki members, and Shikamaru could use his intelligence to strategize for the clan's growth.
In this fanfic, Naruto might start by uniting the Uzumaki clan members. He could use his influence and power to bring back the glory of the clan. Maybe he'd focus on rediscovering lost Uzumaki jutsu and pass them on to the new generation.
Kushina Uzumaki was known for her fiery red hair and strong will. She was a Jinchuriki, just like Naruto, which made her both powerful and a target. Her love for her family, especially Naruto, was unwavering. Even though she sacrificed herself early in Naruto's life, her influence on him was profound.
Karui could be one of the characters. Since she is from the Hidden Cloud Village and has a connection to the Uzumaki clan through her son's relation to Naruto. Another could be Hinata. Although she is from the Hyuga clan, her love for Naruto and the Uzumaki influence on Naruto's life could bring her into the story. Also, Tsunade, as she has a connection to the Senju clan which is related to the Uzumaki clan.
Naruto is likely to be the catalyst. He has the influence and the will to bring together the scattered Uzumaki members.
Well, he could start a family with Hinata and have lots of kids, passing on his Uzumaki bloodline. Then, he could encourage his friends who have some Uzumaki connection, like Karin, to also have families and pass on their Uzumaki genes. He could also set up a school or training center in the Uzumaki land, teaching the Uzumaki ways of life and ninjutsu, which would attract orphans or those who want to be part of the Uzumaki clan.
One aspect to consider in Naruto and Kushina Uzumaki fanfiction is their relationship. Kushina was Naruto's mother. Fanfictions often explore how their bond could have been different if she had survived. For example, she could have taught Naruto more about the Uzumaki clan's secrets. This would have given Naruto an even greater power boost and a deeper understanding of his heritage.