The error message indicates, there is already a remote configured with the same name. So you can either add the new remote with a different name or update the existing one if you don't need it.
First of all Github has a good documentation on renaming a remote to help with this issue.
Check your remote repositories that you're connected to
git remote -v
This should return a list in following format
origin firstname.lastname@example.org:github/git-reference.git (fetch) origin email@example.com:github/git-reference.git (push)
That might help you figure out what the original 'origin' pointed to.
At this moment you could follow either of the below methods to resolve this error based on your requirements.
Remove the origin and your new repository as in
git remote rm origin git remote add origin newrepo-url
If you want to keep the remote connection that you see with the -v, but still want to follow the workflow without having to remember 'github' (or some other name) for your repo, you can rename your other repository with the command:
git remote rename [current name] [new name]
git remote rename origin oldreponame
Once done, you should be able to change origin to new repository with
git remote add origin newrepo-url
You could also use a new name for remote url as
git remote add github newrepo-url
Remember though, everywhere now onwards you'd be using
github as your remote name.
git push origin master should now be
git push github master.