His character would become more detached. Percy is usually very involved and emotional in his relationships, but as Death, he would need to be more aloof. He can't be too attached to the living as his new role demands a certain level of impartiality towards life and death.
If Percy becomes Death in fanfiction, his character undergoes a radical transformation. He becomes more stoic and less impulsive. Percy used to be quick to act and sometimes rash, but as Death, he has to be more calculating. His sense of right and wrong also gets a bit muddled. As Death, he has to deal with the natural order which may not always align with what he previously considered moral. For example, he may have to let good people die because it's their time. This new role forces him to look at the bigger picture of the cosmos rather than just individual lives, and that changes his very essence.
He might become more authoritative. As the Titan King, Percy would have to command respect and make tough decisions. He can't be as carefree as he was before.
His social circle would expand. He'd meet new people in the music industry, from producers to fellow singers. His daily routine would shift from demigod training to rehearsals and recording sessions.
His personality might become more reserved. As a Cullen, he'd have to fit into their more subdued lifestyle. He might lose some of his brashness.
In this fanfiction scenario, Percy's character change would be quite drastic. He would probably start to embrace the more chaotic and power - centric nature of the Titans. His relationships would be in turmoil. For example, his relationship with Annabeth would be severely tested. He might not value the same things he once did, like friendship and the protection of the camp. His new Titan - influenced self could be more self - serving, seeking to gain as much power as possible and not caring about the consequences for those around him. His values would be realigned with the Titans' more cut - throat approach to power and survival.
If Percy becomes influenced by Kronos in this fanfiction, his sense of morality would be greatly affected. He would probably lose his sense of right and wrong which was a big part of his character before. His loyalty towards Camp Half - Blood and his friends would be in jeopardy. He might start to think that the ends justify the means, which is a very Kronos - like way of thinking. And he could become more aggressive and less patient, as Kronos was always in a hurry to regain his power and rule over the world.
He becomes more serious. Gone is the Naruto who is always cracking jokes.
His story changes a great deal. He can't rely on his powers to solve problems. For instance, in battles, he'd have to use normal weapons or his intellect. His relationship with Annabeth would also be different. They might not have the same kind of adventures together. He'd be more in danger from the mythical world since he's no longer a powerful demigod.
His character might become more aloof. As a primordial god, he would be far removed from the normal world of demigods. He'd likely have a different perspective on things like friendship and loyalty. For example, he might not be as quick to jump into a fight for his friends as he used to be, because his new status would bring a different set of responsibilities.
He might become more solemn. As a god, he has more responsibilities. So, he can't be as carefree as he was as a demigod. He would need to think about the big picture all the time.
His character would likely become more hardened. The military life is tough and Percy would have to face a lot of difficult situations. He might become less trusting at first as he'd be in a new environment full of strangers. But over time, he could learn to rely on his new comrades. Also, his sense of responsibility would expand from just protecting his friends and family to protecting his entire unit and his country in the context of the fanfiction.