People who are right-handed rarely have a reason to ponder whether or not a character they love is predominately left-handed or right-handed, because 90% of people are right-handed and society is more or less set up to accommodate them.
Since lefties are a minority both in real life and fiction, even limited representation can feel pretty important.
Luckily, there are a small handful of left-handed individuals who can accommodate—and some of them are among the best anime characters of all time, including Sasuke Uchiha, Edward Elric, and Roronoa Zoro.
Sometimes, the character's handedness is just a fun fact about them. Dabi from My Hero Academia is left-handed, but it doesn't really factor into the story. But Wakatoshi Ushijima of Haikyuu!!'s left-handedness is a major part of why he's such a formidable opponent for the Karasuno volleyball team.
Whether it's plot-relevant or not, these lefties are still pretty awesome.
Since Edward Elric lost his hand in a freak alchemy accident, it's unclear whether or not he originally viewed himself as a lefty. In his post-accident life, his left arm is his only real choice, and he uses it to perform any task that requires more precision than his automail arm can handle.
Haruko Haruhara is a motorcycle-riding, guitar-throwing alien who has nefarious motives for interfering with Naota Nandaba's life. Whether she's hurling Naota into the air or fighting aliens with her guitar, she's doing it all with her left hand.
Roronoa Zoro used to be a bounty hunter, but now he's a member of the Straw Hat crew. He's an experienced swordsman who prefers to use his left hand when it comes to single-sword fighting, but is able to use his right hand during instances where he needs to use two weapons at once.
Sasuke Uchiha is a powerful and deeply troubled ninja who can perform a variety of impressive attacks. He uses his left hand to perform ninjutsu hand signs and wield various weapons.
His left-handedness is proven concretely when Hagoromo asks for his dominant hand and he holds up his left.