Change Name of Availability Group Replica
I want to change the name of an Availability Group Replica because [paraphrased] the name we want it to be is actively being used by a production reporting server [sic]


Personally the name of the nodes shouldn't really matter. Yes, I get naming conventions and whatnot, but at some point (just like which node in a cluster owns a specific role) there is diminishing returns. This is one of those times where you're going to put way more effort into changing it than I personally believe you'll get out of it.


  Not seeing a lot of documentation on this.


I'll add it to my documentation list, and because of this I'll go ahead and answer it here, hoping others may find it.

The Overall Logical Steps

Please note that this does not cover if the node is acting as a forwarder in a distributed availability group.


Remove the node from the AG if it's part of it.
Remove the node from any Read Only Routing (ROR) configurations.
Disable Always On Availability Groups from the SQL Server Configuration Manager/Powershell if it's enabled.
Remove any clustered applications from the Windows Server Failover Cluster Node (WSFC). This includes FCI's acting as part of an AG. You don't have to remove local installs of SQL Server, but you will have to follow the renaming items by dropping and adding the server name. 
Evict the node from the WSFC.
Rename the computer and double check the AD computer object is successfully renamed and replicated to other DCs before continuing. 
Join the node to the WSFC under the new name.
Install any clustered services or applications removed in step 4. Also enable Availability Groups from the SQL Server Configuration Manager/Powershell.
Add the node to the AG.
Update any ROR configurations.