There's a simpler approach which was tested in Visual Studio 2013 Update 1 and applicable for TFS-connected projects:
- Open Visual Studio, but let the solution be closed.
- Open Source Explorer and rename the desired folder (the solution will be closed for you if you didn't already close it first).
- Right-click on the solution (from Source Explorer also) and select check-in.
- Open the solution. You'll be told that there're new projects added. Accept to get the changes.
- Remove the project from the solution and add it again, and then check-in.
- Check that the internal references are OK.