Remotes are just named URLs in .git/config. Rename:
git remote rename old-name new-name
Remove:
git remote remove old-name
Change the URL (don't bother removing/re-adding):
git remote set-url origin git@github.com:org/repo.git
git remote set-url --add --push origin git@github.com:org/repo.git # keep the original push URL
git remote set-url --add --push origin git@gitlab.com:org/repo.git # add a second push URL
The last one — multiple push URLs — lets you mirror a repo to multiple hosts on every push. Common for OSS dual-hosting on GitHub and GitLab.