Maybe an organization that specializes in using the Sharrigan for malicious purposes. They don't want Naruto to expose their secrets, so they send their Sharrigan - users to hunt him down. This organization could be made up of power - hungry individuals who will stop at nothing to achieve their goals.
Maybe Naruto runs away from the Sharrigan because he is framed for a crime he didn't commit. The Sharrigan - wielding enemies believe he has done something wrong and he has no choice but to flee. As he runs, he meets new allies who help him clear his name and also understand the true nature of the Sharrigan better.
He could meet other rogue ninjas. These are ninjas who have left their villages for various reasons, and they might be on a similar journey as Naruto. They could either help him or try to take advantage of his situation.
In a Naruto fanfic where Naruto runs away from Kushina, it could be due to various reasons. Maybe he feels misunderstood. For example, Kushina might be too strict with him in the fanfic's storyline, not allowing him to pursue his own ninja way freely, so he decides to run away to find his own path and prove himself.
In a 'naruto runs away fanfic', one possible plot could be that Naruto runs away after feeling misunderstood by the village. He might go on a journey to find a place where he can truly belong. Along the way, he could meet new allies or enemies. For example, he might encounter a group of outcasts who are also on the run from different villages. They could team up and form a sort of 'runaway family' where Naruto learns new skills and perspectives outside of the Hidden Leaf's teachings.
Maybe he's running away from the pressure in the village. There are always high expectations on him, and he might feel suffocated and need some time alone to figure things out.
At first, Itachi might be a bit distant, but as they run away and are forced to rely on each other, a deeper connection forms. Naruto's positive attitude would gradually break down Itachi's walls. They could start sharing their hopes and fears. Itachi might open up about his family and his regrets, and Naruto would listen and offer his own perspective. This sharing would strengthen their bond, and they would become like brothers, protecting and supporting each other.
One consequence could be that his friends worry about him a great deal. They might go on a search for him, which could put them in danger as well. After all, they care about Naruto deeply and won't just let him disappear without trying to find him.
They might run away to avoid a conflict that their villages are about to be dragged into. Naruto and Sasuke, being the powerful ninjas they are, don't want to be used as tools in a war, so they decide to run away.
Next, Naruto might meet new allies. He could encounter other ninjas who have also had run - ins with their families. They could form a group and train together, becoming stronger and more independent from their families.