“Renaming” a remote branch in git, as indicated by the link you provided, is really just deleting a branch, followed by pushing a new one with the same commit hash but a new name. If you have a pull request open for branch patch-1, when you delete that branch, the pull request will be closed.
So, no you can’t rename the branch with a pull request open without deleting the branch and removing the pull request. However, there’s nothing stopping you from doing that, pushing a new branch with a new name, and creating a new pull request.