Go to the project in question an open the " Settings" page. Change the Repository name and click on the Rename button. Github will present you with a warning dialog. If you're renaming a repository that multiple people use you'll want to make sure you've given them a heads up.

Next you need to drop and re-add the remote on your local copy. Or remove and re-clone, but this is the git way:

git remote rm origin  
git remote add origin git@github.com:<USER>/<REPO>.git  
git pull # this will provide an error, fix:  
git branch --set-upstream-to=origin/<BRANCH> <BRANCH>  
git pull  

Swap in your details for <USER>, <REPO> and <BRANCH> and you should be good to go!