Rename the branch will be useful once your branch is finished then. Then new stuff is coming, and you want to develop in the same branch instead of deleting it and create the new one.
From my experience, to rename a local and remote branch in gitGit you should do the following steps.
Quoting from Multiple States - Rename a local and remote branch in git
1. Rename your local branch. ###1. Rename your local branch
If you are on the branch you want to rename:
git branch -m new-name
If you are on a different branch:
git branch -m old-name new-name
2. Delete the old-name remote branch and push the new-name local branch. ###2. Delete the old-name remote branch and push the new-name local branch
git push origin :old-name new-name
3. Reset the upstream branch for the new-name local branch. ###3. Reset the upstream branch for the new-name local branch
git push origin -u new-name