Allow images instead of names.
Even if it just allowing [img] tags with a pre-existing urls, that would help out a lot.
Sometimes an image work better then a name. Giving an example I am currently running a forum tournament for a retro fighting game. The game allow you to pick a character then set up the stats. There only about 10 characters on the game. Each forum member is allow to have three character each. While currently I am asking each character to be mark with a "tag" (Candy, Bones, Icedude, etc) so I can keep track of them it would be much easier to just use images. Player cards often exist for things like Pokemon and Super Smash Brother Brawl anyway.
Allowing images would be enough, being able to upload them on your site would just be a bonus.
I am aware that depending on the image it could mess with the formatting of the bracket. Allowing a name then an image so you can see the name on the bracket but the image on report scores page could be a easy and simple fix for that though there are many ways of doing it.
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Zelkova commented
Too add on this, for voting polls like "Challonge Favorite Pokemon" for example it would be nice to keep the names on the bracket but have the users see exactly what they are voting for in the voting part.
To give an example of how a picture may be useful when voting:
Naruto, Grown up Naruto, Sage Naruto, One-tail, Four-tails, 8 tails, blah blah blah Naruto? Just because games have gotten to the point where they don't need to use palette swaps that don't stop them from reusing the same character.
Dragon Ball Z have like 6 different Gokus, Naruto as seen above have more then that, even Pokemon have some of them with different forms even if ignoring shiny colors or gender differences.I am aware your site was made with the idea of player vs player matches but there are games that allow CPU vs CPU and does so for a reason regardless how pointless it may seem. The choice of allowing pictures wouldn't hurt anything at the very least.