• rename a local branch - must be currently in the branch to rename
    git branch -m new-name

  • Delete the old-name remote branch and push the new-name local branch.
    git push origin :old-name new-name

  • Reset the upstream branch for the new-name local branch. - switch to the branch
    git push origin -u new-name

shortcut

git branch -m old_branch new_branch         # Rename branch locally
git push origin :old_branch                 # Delete the old branch
git push --set-upstream origin new_branch   # Push the new branch, set local branch to track the new remote

References