No. Do not touch the replica, do not rename it, nothing. Just leave it.
The snapshot on the master image is used to create the unique replica for each linked clone pool. If I have a VM with 3 different snapshots (say, each has a different background) then those will be used to create 3 different replicas.
Let's say that SP14 (totally made up service for the sake of an example) comes out for Windows 7 and I want all my link clones to have it, I would recompose the pool. This effectively creates a new replica and recreates the linked clones by associating them to the new replica. Old ones aren't deleted until all the linked clones are on the new ones. If this is a dedicated linked clone pool that has persistent disks those are maintained and moved over to the new linked clones.
You may want to check out the free videos we/I made at http://www.vmwarelearning.com Those might help explain some of this.