I have changed the name of repositories before, and I'm doing it again right now ;-)
Edit the name using the built-in feature under the "Settings" tab at the top of your GitHub repository page. Then go to your local repository and rename the remote. Like this:
First remove it:
git remote rm origin
then add back the new name
git remote add origin git@github.com:"yourname"/"projectname".git
If you have recent enough git version you should use set-url command:
git remote set-url origin git@github.com:"yourname"/"projectname".git
Now it should be good to go.