How do I rename an existing branch in a Git repo?

I want the current branch to have a new name.

Assuming you're currently on the branch you want to rename:

git branch -m newname

This is documented in the manual for git-branch, which you can view using

man git-branch

or

git help branch

Specifically, the command is

git branch (-m | -M) [<oldbranch>] <newbranch>

where the parameters are:

   <oldbranch>
       The name of an existing branch to rename.
<newbranch>
The new name for an existing branch. The same restrictions as for <branchname> apply.

<oldbranch> is optional, if you want to rename the current branch.