Yes,

the feature move exists to rename the branch locally

git branch --move <old_name> <new_name>

but to push it, you must delete the old and push the new

git checkout <new_name>
git push origin [--set-upstream] <new_name>
git push origin --delete <old_name>

--set-upstream is optional, it configure the new local branch to track the pushed one

You can use the following shorthands:

• move locally (--move) :

    git branch -m <old_name> <new_name>
  

• push new branch (--set-upstream, optional) :

    git push origin [-u] <new_name>
  

• delete (--delete) :

    git push origin -d <old_name>
  

NB.

Thanks to torek's comment:

Worth mentioning, by the way, is that you should

1. notify other users who share the upstream that you will be doing this, and
2. do this in the order shown (set new name, then delete old).

The reason for #1 is that those users will need to adjust.

The reason for #2 is mainly just efficiency: it avoids having to re-copy objects to an upstream repo that drops commits on branch deletion (most bare repositories do that, and most repositories that accept pushes are bare)