I know this topic is slightly old but I feel the urge to put in my thoughts.
I never thought his cap said Curly Brace on it. I know his name was originally going to be that, but I'm pretty sure his hat says Quote on it, or possibly some robot identification code?
The reason I don't think it says Curly Brace is A) Curly did not notice it when he first saw her in the Sand Zone. Then again, there is no proof Curly can read -- however I presume she can since Quote was able to read things Kazuma and Sue had written on the computers. Sue said the language on his cap was "not one they have on this island," so you can assume she recognized it -- and since Quote was made on the planet below the island, it's safe to assume the language on his cap was the language down there, the one Sue and Kazuma originally speak and write in -- which Quote could read. Ergo, one can assume Curly can read it as well.
B) Why would Quote's hat say Curly Brace, when one, that's not his name, and two, there is nothing that links Curly to Quote in the same fashion -- I suppose one could include the iron bond, but it seems there's only one of those.
And, uh, yup. Those are my thoughts. I know it's been officially confirmed by Pixel that the hat says Curly Brace, but I think it maybe makes more sense if it said Quote. I always just assumed it did when playing after I found out his name, anyhow.