1. Rename your local branch.
If you are on the branch you want to rename:
git branch -m NEWNAME
If you are on a different branch:
git branch -m OLDNAME NEWNAME
2. Delete the old-name remote branch and push the NEWNAME local branch.
git push origin :OLDNAME NEWNAME
3. Reset the upstream branch for the NEWNAME local branch.
Switch to the branch and then:
git push origin -u NEWNAME