Question: `git mv` renames a file or directory in a repository. How do I rename the Git repository itself?

Answer: 
A Git repository doesn't have a name. You can just rename the directory containing your worktree if you want.
To be simple, just remove that Eclipse Project (not choose content on disk), then re-import the project again. 

Eclipse will identify the project connected to Git and put it in Git perspective view.

It works like a charm.