I've sent my application in already, I was never requested to provide documentation for my name, age, or gender. Keep in mind that I have my birth name and gender down on the application, but I don't think you'll run into any problems with the situation you describe. When the app says name on BC, I assume that is to say "Your legal name", so someone doesn't put down a nick name or something.
The only issue I might foresee is if any documents sent by your highschool/recommenders/whatever conflict with your stated name and gender.