Here's how to handle renaming when using Xcode 4:
Go to App Game Kit/IDE/templates.
Copy and paste the folder template_ios_xcode4.
Rename the folder template_ios_xcode4 copy to MyGame.
Go into the MyGame folder and open the file template.xcodeproj.
When Xcode has opened and the project is ready for editing, show the Project Navigator, click on the blue icon for the template and hit return, now enter MyGame and press return.
A dialog will pop up asking you to rename project contents items, press the Rename button.
At this point Xcode may ask about taking snapshots, choose Enable or Disable dependent on your preference.
Now return to the Project Navigator, click on the blue icon for MyGame. To the right you will see a window showing Project - MyGame and Targets - MyGame. Select MyGame listed under Targets.
You will see a selection of tabs over to the right including Summary, Info, Build Settings, Build Phases and Build Rules. Select Build Settings.
In the search box type "product name". Double click on the search result and replace template with MyGame and press the Done button.
Xcode 3 should be fairly similar.
As for the icon this may be something in the plist that is overriding icon@2x.png.