In our steps to rename a replica set, we include the commands to rename a replica set using system.replset.

We had a recent S1 Support Case where a customer had root and dbOwner for local but wasn't able to perform this and was under time pressure to do so. I think it would be helpful to list what permissions are needed, if you can't do this with root or dbOwner.

For instance the following role contains the necessary permissions:

db.runCommand( { createRole : "replsetRole", privileges : [ { resource : { db : "local", collection : "system.replset" }, actions:["find","update","remove"]}], roles : [] })