Yeah of course you can access the SD card to do whatever you want (read, write, create files and folders, renames them...). It will depend on the SD library you use. The more features it has, the more memory it will take.
You can find a list of the most common SD libraries for Arduino (...and Gamebuino as well) on the wiki :
http://gamebuino.com/wiki/index.php?title=SD_cardReference of the official Arduino SD library :
http://arduino.cc/en/Reference/SD