He might become more confident. Having a powerful dragon quirk could make Izuku realize his own strength, and he'd carry himself with more assurance. For example, he wouldn't be as shy when speaking up in class or to other heroes.
His personality might become a bit more fiery, literally and figuratively. The dragon quirk could give him a short temper at times, especially when he's feeling threatened or when someone is being unjust. However, he would also learn to control this side of himself. He could also develop a sense of pride in his quirk, not in an arrogant way, but in a way that makes him want to show what he can do with it for the good of others. And since dragons are often associated with mystery, he might become a bit more enigmatic to those around him, with a certain air of the unknown about his actions and abilities.
His personality could be split. On one hand, he would still have his core values of heroism and kindness. But on the other hand, the dark quirk could bring out a more ruthless side. He might find himself having internal debates between using his power in a traditional heroic way or succumbing to the darker impulses that the quirk brings. This internal struggle would be a major part of his new personality in the fanfiction.
His relationship with Bakugo might change. Bakugo could be jealous of Izuku's unique quirk at first. But later, they might have to team up for an underwater mission. Izuku's friends from school could also be in awe of his mermaid quirk and might want to learn more about it.
His relationship with Bakugo might change. Bakugo, who used to look down on Izuku, might now be a bit jealous or even more competitive as Izuku's Dragon Slayer quirk is very powerful. With his friends like Uraraka, she could be in awe of his new quirk and support him more actively in battles. Izuku might also attract the attention of some of the more powerful heroes in training, who want to team up with him because of his unique ability.
Some characters might be immediately terrified. They could avoid Izuku or even try to drive him away. For example, classmates who don't understand his quirk might spread rumors about him.
His relationships with his friends would likely become more complex. If he starts using his time quirk to change things, his friends might not remember the original timeline, but Izuku would. This could create a sense of isolation for him as he holds memories that no one else does.
It might also change his relationships with other characters. His friends could be both amazed and a bit envious. And his enemies would start to see him as an even greater threat. For example, Bakugo might feel more pressured to compete with Izuku who now has an additional powerful quirk.
The Gamer Quirk also changes Izuku's relationship with others. He can now offer unique insights based on his quirk. For instance, he might be able to analyze a villain's attack pattern like it was a boss fight in a game. His friends and allies can then use this information to their advantage. This makes him a valuable member of any team. At the same time, it also means that he might be seen as a bit of an oddball because his thinking is so different from the norm. But overall, it helps him form deeper connections with those who understand and appreciate his quirk.
In a fanfiction, the development of Izuku having a black fire quirk can be really multi - faceted. First, the visual aspect of the quirk can be described in detail. The black fire could have a smoky, otherworldly look that sets it apart from normal fire. Emotionally, Izuku could struggle with the fact that his quirk is so different from what he expected. He might feel like an outcast among his peers. Then, there could be a story arc where he discovers a hidden power within the black fire quirk. For instance, he might find out that it can absorb other forms of energy. This would not only make his quirk more powerful but also open up new storylines about him learning to use this new aspect and facing new enemies who are interested in his unique ability.
There's a fanfic titled 'Izuku's Wolfish Abilities'. In this, his wolf quirk gives him enhanced senses. He uses these to his advantage during battles and rescue missions. The story also delves into how his quirk influences his relationships, especially with Bakugo and Todoroki.
One implication could be a change in his relationships. His friends might be initially afraid or distrustful. For example, Bakugo could see this as a sign of Izuku being a real threat now, instead of just a rival. Also, the teachers at UA might have to deal with a whole new set of problems regarding Izuku's training and control of his dark quirk.