If you want to rename a branch while pointed to any branch, do:

git branch -m   
If you want to rename the current branch, you can do:

git branch -m  
If you want to push the local branch and reset the upstream branch:

git push origin -u  
And finally if you want to Delete the remote branch:

git push origin --delete  
A way to remember this is -m is for "move" (or mv), which is how you rename files. Adding an alias could also help. To do so, run the following:

git config --global alias.rename 'branch -m' 
If you are on Windows or another case-insensitive filesystem, and there are only capitalization changes in the name, you need to use -M, otherwise, git will throw branch already exists error:

git branch -M