If you have a 2 node replica set (IP1 and IP2), here are the steps you
can do to rename once you have deleted your local.*.
Shutdown mongod on IP1 and IP2. Ensure local.* is not present.
If IP1 has the latest copy of your data, create a backup of all your
data files from IP1. Now delete only local.* from its data directory
(if still present).
Now start mongod on IP1 with the new replset name. Run rs.initiate
with just IP1 in its config.
On IP2, ensure that you remove all data files. Start mongod with the
new replset name. Connect to IP1 and do rs.add("host:port") to add IP2
to the replset. Let it resync from IP1.
Also make sure you either add a 3rd RS member or an arbiter.