For context, I'm writing a fantasy story.
This is very common in Japanese Anime/Manga. Every fighter may have his own fighting style, and that style would reflect traits like treachery or bravery. This is probably better expressed in graphic than in writing, but in literature this is used too.
Here are the things you can pick for your characters:
- Weapons choice (sword/hammer/bow/daggers)
- Direct confrontation vs evasion vs fleeing
- Careful planning vs rushing in
- Improvising, use of "props" like rocks, sand, water
- Wounding the enemy minimally vs dealing mortal blows vs maiming
- Stopping when the opponent is down vs pressing on with advantage
I would say yes to that, given that whenever there are superhero fights in movies, they always say something to go along with what they're doing, but that shows their personality. Take Big Hero 6 as an example, when GoGo is wheeling around and fighting the Kabuki mask guy, she says "Woman Up!" She said that earlier in the movie when Hiro was presenting his microbot idea.
So yes, I think a characters' fighting style should express their personality.