If Naruto becomes a Red Lantern, his ability to fly, which is a common power among Red Lanterns, would be a new addition to his skill set. This would give him an advantage in combat and mobility. His sensory abilities, which are already good as a ninja, could be enhanced further by the Red Lantern power. He might be able to sense emotions more strongly, especially rage, which could help him in battles or in finding allies or enemies.
His physical abilities would likely be enhanced. Red Lanterns have increased strength, speed, and durability. Naruto already has great physical prowess as a ninja, but as a Red Lantern, he could become even stronger. His ninjutsu might also change. For instance, his rasengan could be infused with red energy, making it more powerful.
Naruto's most famous ability, the Nine - Tails chakra, would interact with the Red Lantern power in complex ways. Maybe the Nine - Tails would be affected by the rage - based Red Lantern power and become more uncontrollable at first. But over time, Naruto could learn to use both powers in harmony. His shadow clone jutsu could also be improved. He could create clones that are also Red Lanterns, each with their own share of the red energy, multiplying his combat effectiveness.
Naruto's personality would adapt to fit the new role. His existing positive traits like his courage and his ability to make friends would help him in the Green Lantern Corps. He'd be more of a team player perhaps, learning to work with beings from all over the universe. His impulsive nature might still be there, but he'd learn to control it better with the discipline that comes with being a Green Lantern. And his overall goal would shift from becoming Hokage to being a great Green Lantern and protecting the cosmos.
Naruto's chakra - based abilities would probably be combined with Deathstroke's combat skills. For example, he could use his Rasengan while also making quick, precise slashes with swords like Deathstroke. His ability to sense chakra could be enhanced in a way that mimics Deathstroke's heightened senses in combat.
Naruto's perception abilities might improve. The Green Lantern ring gives the user access to a lot of information. He could use this to detect enemies more easily, similar to how he uses his sage mode to sense chakra. Also, his ability to communicate and connect with others could be different. He might be able to use the ring to communicate across long distances, which would be useful in both his ninja world and in any Green Lantern - related scenarios.
His mobility would be enhanced. He could fly around like Green Lanterns do, which is a huge change from his normal ninja running and jumping. He could also use the ring to create shields, protecting himself from attacks that his ninja gear might not be able to handle.
His combat style would change drastically. Instead of relying solely on ninjutsu, he'd be using the powers of the Lantern Ring. For example, if he had a Blue Lantern Ring, which is associated with hope, his attacks would be filled with a sense of optimism and might even inspire his comrades in battle more than before. His enemies would be facing a very different Naruto, one with powers that they may not have any prior knowledge of how to counter.
Naruto's character would gain a new sense of responsibility. As a Green Lantern, he'd have to abide by the Corps' rules and uphold justice on a much larger scale. This might make him more serious at times, but his core of being a fun - loving and determined person would still remain. He'd also learn to work in a team with other Green Lanterns, which could be different from his experience with his ninja teams as they come from diverse backgrounds.
His already positive personality would become even more so. He'd be like a beacon of hope. He might be more focused on bringing out the best in others, since that's what Blue Lanterns do.
If Naruto was raised by Slenderman in fanfiction, his abilities would change drastically. His chakra control might be influenced by Slenderman's otherworldly energy. He could gain the ability to manipulate the environment in a more spooky way, like making the air feel cold and heavy around his opponents. Also, his Rasengan might take on a different form, perhaps with a dark, swirling energy around it.
His physical abilities would likely improve greatly. Whis could train Naruto to have better speed, strength, and agility, much like how he trains Goku and Vegeta in Dragon Ball. Naruto might also gain the ability to sense ki, which would give him an extra sense in battle.
His physical strength might increase. Dwarves are often depicted as strong, and living among them could mean Naruto has to do a lot of physically demanding tasks like mining or lifting heavy objects. So, he'd likely have more brute force.