So... off I went to discover the steps involved in the renaming process and it boiled down to TWO major steps.
1: Copy and rename the .spritebuilder file (bundle).
2: Once duplicated, rename it - make sure you conform to the standard SpriteBuilder limitations (USE NO SPACES).
3: Right-click and choose "Show Package Contents" to open the bundle folder. Just rename the .ccbproj file.
4: Double-click the Xcode project to open Xcode and proceed to STEP TWO.
In our example we are going to rename "StarterGame.spritebuilder" to "AwesomeProject.spritebuilder".
1: Once open in Xcode, perform a normal rename via the "Name" field in the right column.
Afterwards I usually close and exit Xcode then open the new project in SpriteBuilder, publish and use the shortcut to open Xcode.