The feature (when you right-click the Task Bar icon) is called a Jump List.
For some reason, Windows doesn't cooperate with simple solutions to this (like just right-clicking and renaming the pinned item).
You can work around this by pinning a renamed shortcut to the Jump List.
- Before you begin, unpin the folder you want to rename. If it appears in the frequent list when you right-click, you'll also need to right-click it and remove it from the frequent list.
- Create a shortcut to the folder you want to pin. An easy way is to right-click and drag the folder to your Desktop (or another location) and select "Create shortcuts here."
- Rename the shortcut as you'd like it to appear on the Jump List.
- Drag and drop the shortcut onto the Explorer icon on the Task Bar (unlike other shortcuts, folder shortcuts must be dropped directly onto Explorer and not just a blank spot on the Task Bar).
The folder should now be pinned with the shortcut name. You can delete the shortcut once you've pinned the folder, it was just a middle-man.
This works on Windows 7, 8, and 8.1.