Q: Hyper-V Replica is enabled on my virtual machine (VM), but the VM has the same name on the source and target Hyper-V server--can I rename the replica VM?
A: Yes. Once the Hyper-V Replica replication has been enabled and running, it's fully supported to rename the replica VM. This won't cause any interruption to the replication process since the VM GUID is used between the source and target and not the VM name.
You might also look at "Configuring Hyper-V Replica in Windows Server 2012." Also, here's something you probably shouldn't change on Hyper-V Replica: "Q: Can I change the replication frequency of Hyper-V Replica?"