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

Answer: 
In a new repository, for instance, after a `$ git init`, the .git directory will contain the file .git/description.

Which looks like this:

`Unnamed repository; edit this file 'description' to name the repository.`

Editing this on the local repository will not change it on the remote.
Open git repository on browser, got to "Setttings", you can see rename button.

Input new "Repository Name" and click "Rename" button.