Well, one possibility could be that Kushina takes Naruto away to protect him from the dangerous world of shinobi. Maybe she wants to raise him in a peaceful place away from the constant threats and battles in the Hidden Leaf Village.
There might also be other characters involved. For example, Minato might make an appearance in flashbacks. Since he was Kushina's husband and Naruto's father, his presence could be important in terms of the backstory. Also, characters from the Hidden Leaf Village might be mentioned or even try to find Naruto and Kushina, like Iruka Sensei who has a special bond with Naruto.
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.
Perhaps Naruto feels that Kushina is being overprotective. He wants to prove his independence and go on his own adventures without her constant supervision, so he decides to run away.
Naruto's character development would likely be more influenced by Kushina's values. He might be more empathetic towards certain things that Kushina cared about. For example, if Kushina had strong feelings about a particular clan or group, Naruto could grow up with a similar mindset.
Kushina could develop in terms of her relationship with Naruto. At first, if she is just taking advantage, it might be a one - sided relationship. But as the story progresses, she could grow to truly care for Naruto as a mother figure. This could be shown through her sacrificing her own interests to protect Naruto or by being more empathetic towards his struggles.
She would influence his growth by instilling in him the values of the Uzumaki clan. Naruto would learn about loyalty, perseverance, and the importance of family. These values would make him a more well - rounded ninja. Also, Kushina could teach him some unique Uzumaki jutsus that would give him an edge in battles. She might also encourage him to explore his heritage more, which could lead to new powers or abilities.
He might face a lot of danger on his own. Since he's running away from Kushina who would usually protect him, he could encounter stronger enemies that he's not fully prepared to face.
One possibility is that Minato takes Naruto away to a secret training ground. There, he could start to teach Naruto advanced jutsu that he never got to pass on before. This would be a way for Minato to make up for lost time and help Naruto become even stronger.
Naruto might discover new Uzumaki techniques. Since the Uzumaki clan was known for their strong sealing jutsu, he could learn some advanced sealing techniques during his visit to Whirlpool. Maybe he'd find a special scroll left by his ancestors that contains a powerful jutsu.