I don't want to rename a remote branch, as described in Rename master branch for both local and remote Git repositories.
Instead, I want to use the simplest way to rename a local branch, which hasn't been pushed to a remote branch.
If you want to rename a branch while pointed to any branch, do :
git branch -m <oldname> <newname>
If you want to rename the current branch, you can do:
git branch -m <newname>
A way to remember this, is
-m is for "move" (or
mv), which is how you rename files.