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. 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 <newname>