He might become more brooding. The need to control his bloodlust could make him withdrawn.
Harry's confidence would likely grow in a different way. Instead of the boy - who - lived bravado, he'd have a more quiet and self - assured confidence. He'd know that he has powers and knowledge that others don't, and this would show in his demeanor. He might be less impulsive and more calculating, which could both help and hinder his relationships and his ability to protect the wizarding world.
He might become more authoritative. Since he has the power of an emperor, he would need to make tough decisions and be more assertive in his commands.
He might become more stealthy and reserved. Instead of being as open as he was in the wizarding world, he'd have to be more secretive as a ninja.
He might become more brooding. The new powers and the vampiric nature could make him a bit more withdrawn as he tries to understand and control his abilities. But his core of kindness would still be there.
He might become more withdrawn at first. The knowledge of his new, blood - thirsty nature could make him afraid of hurting those he cares about. But over time, he could become more confident in controlling his vampire side and use his newfound power to be more assertive.
Well, he might gain superhuman strength and speed. He could also have the ability to influence minds, which would be a huge advantage. His magical abilities might be enhanced or changed in some way too. And he would probably have to deal with the thirst for blood, which could create a lot of internal conflict.
His character would become more complex. He'd have to struggle with his newfound thirst for blood, which could make him more brooding. He might become more isolated as he tries to hide his vampiric side from his friends. His sense of right and wrong would be challenged as he has to deal with the darker aspects of his new existence.
His sense of responsibility would likely increase even more. Harry has always been responsible, but as a priest, he would feel accountable for the spiritual well - being of others. He would become more solemn and less impulsive perhaps. His Gryffindor impulsiveness might be toned down as he takes on a more serious religious role.
His personality might become more reserved. Growing up with a Shinigami would expose him to different values than the normal wizarding ones. He might not be as quick to trust or be as carefree as in the original story. Instead, he'd be more cautious and perhaps a bit more brooding, always thinking about the deeper meaning of things and the consequences of actions.
His personality would be greatly influenced by the forest environment. He would be more wild and free - spirited. Growing up away from the constraints of wizarding society, he would have a different set of values. He would be more empathetic towards animals and nature, seeing them as equals rather than something to be used. He would also be more solitary at first, but once he meets others, he would form very deep and loyal relationships as he values connection on a deeper level.