I was asked what my race was, and I chose...but then I managed to exit without setting a name, gender...anything else. So now I'm a dude called "Prisoner". I'd hate to play the whole game with such a lame name. Am I going to be given an opportunity, like in Oblivion, to change these things again at some point, or do I need to start over, or...?
In the PC version, /showracemenu worked fine for me, and I successfully changed my appearance (eye-color, mainly), without affecting my skills, level, or anything like that (I recall in Oblivion there was a fairly convoluted way to do it -- this is much easier). I've heard changing your race is a bad idea though.
I've heard there's a converter to change your savegame from XBox 360 to PC and back. If you can find one of those, and have a friend (or know someone online) with the PC version, you could give them the savegame, run the console command, adjust your name, then convert it back to XBox 360.
Seeing as it's a single-player game, I really don't see any tos issues with a converter (you can supposedly do this to redo your perks, or give yourself a billion health, etc., as well). However, having never seen or used it, I've no idea if it might corrupt your savegame later.
Another possibility might be to hex-edit the data on the XBox 360 version of the savefile from your computer. I can't find my character name this way, but someone better at that sort of thing might be able to find it (editing the name on the first line of the file just changes the text displayed on the save/load screes, not the name of the player container). Your best luck in that case would be to make the new name eight characters long, or there might be formatting issues.