She becomes more confident. With the Tenseigan, Hinata has a new source of power. This newfound strength gives her the confidence to be more assertive, not just in battle but also in her relationships. For example, she might be more outspoken in the ninja council meetings where she used to be quiet.
One popular storyline often involves Hinata somehow obtaining the Tenseigan and how it affects her relationship with Naruto, especially considering Naruto has the Rinnegan. Maybe they team up in a new and powerful way against an old foe.
Yes, in some fanfictions Naruto can be given the Tenseigan. Writers often like to experiment with different power combinations for characters, and giving Naruto the Tenseigan is one such creative idea. It can lead to very interesting plot developments, like new ways of fighting and different relationships with other characters.
If Naruto had the Tenseigan in fanfiction, he would likely become extremely powerful. His combat abilities would be enhanced, as the Tenseigan gives access to powerful jutsu. He could also gain new ways to sense chakra and enemies, making him even better at tracking and anticipating attacks.
One implication is that he becomes much more powerful. The Rinnegan gives him access to powerful abilities like the Six Paths techniques, which would change the power dynamics in battles in the fanfiction. He could now face stronger enemies more easily.
A plotline could involve the Tenseigan being a key to unlocking a hidden realm. Since it was neglected, it has been slowly building up power. When the main character finally taps into it, they are thrust into this new realm, full of unknown dangers and allies. There, they must learn to master the Tenseigan's power to find a way back home and use this new - found knowledge to better the ninja world.
Maybe an evil organization that has its own plans for the Tenseigan. They have been secretly manipulating events to ensure that the Tenseigan remains neglected so that they can steal it and use its power for their own dark purposes. The main character would have to fight against this organization to protect the Tenseigan and its potential for good.
In Naruto fanfiction, the Rinnegan in Naruto is often portrayed in really cool and powerful ways. Some fanfics might give Naruto the ability to use all the Rinnegan powers to their fullest extent right away, like being able to effortlessly summon the Gedo Statue or use the Deva Path powers without any drawbacks. It's a way for writers to explore new storylines and make Naruto even more of a badass than he already was in the original series.
Another possibility is that it's a result of some strange chakra experiment gone wrong (or right). Scientists in the Naruto universe are always dabbling in chakra research. Maybe an experiment meant to enhance her natural abilities instead gives her the Rinnegan, and she then has to learn to control it quickly to avoid being consumed by its power.
If Naruto got the Rinnegan, he might become more cautious. The power of the Rinnegan is so great that he would realize he needs to be more careful with it. He wouldn't be as brash as before.