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.
There's a possibility that he meets other Jinchuriki. Jinchuriki are those who have tailed beasts sealed within them like Naruto. They could be on the run too, or they could be looking for Naruto. Meeting them could lead to a sharing of experiences and knowledge about how to live with the power of the tailed beasts.
He might meet some of his distant Uzumaki relatives. There could be elders or other Uzumaki clan members who have valuable knowledge about his family and their special abilities.
He could meet some of Iwa's powerful ninjas. Maybe Onoki, who could either see him as a threat or an opportunity. There might also be some young Iwa ninjas who are curious about Naruto and his abilities.
He would surely meet Gaara. Gaara has had his own struggles and he might be able to understand Naruto on a deeper level. They could form an even stronger bond than before, with Gaara helping Naruto hide from those who might be looking for him in Suna.
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.
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.
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.
Naruto could meet the Raikage in this fanfic. The Raikage, being the leader of Kumo, would surely take notice of Naruto's arrival. They might start off on a tense note, as Naruto is from a different village, but later develop an understanding.
He could meet some rogue ninjas. These ninjas might either try to harm him or, in some cases, offer to help him on his journey. They might have their own reasons for being in the area between Konoha and Kumo.
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.
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.