If you have already pushed the wrong name to remote, do the following:
Switch to the local branch you want to rename
git checkout <old_name>
Rename the local branch
git branch -m <new_name>
Push the <new_name>
local branch and reset the upstream branch
git push origin -u <new_name>
Delete the <old_name>
remote branch
git push origin --delete <old_name>
This was based on this article.