This is at least partially addressed in upcoming VS2013 Update 2, which is out in preview form. Once you moved/renamed the solution, you introduced a "branch" operation in TFS, and the original indicator only showed the current info, not working back through any branch info.
In VS2013 update 2, we added more support to handle branch operations and hopefully show more information than you have now. I thought there was a blog post about the branch info, but the only one I can find is a related post about the new incoming changes indicator:
http://blogs.msdn.com/b/visualstudioalm/archive/2014/03/03/new-codelens-indicator-incoming-changes.aspx
(my team used to be responsible for the changes,etc indicators, but we aren't any more, so i'm not sure exactly if your issue is entirely fixed there or not.)
Edit: note that the indicator only shows data it gets from the server, so in order to see incoming changes or branch information in any of the TFS powered indicators, you also need the corresponding update to the TFS server that drives this info.