Recovery :: Restore Clustered Server Into Single DR Server

I'm working to test out a recovery scenario involving a SQL 2008 R2 2 node cluster.  I want to restore it to a standalone server.  The nodes are VMware VMs using physical RDM for the shared storage.  Using Veeam as the backup tool.  Veeam doesn't work with physical RDM so I'm dumping the databases (all Simple) elsewhere to be picked up and replicated with Veeam.  No problem there.  For my DR I have a vanilla 2008 R2 server being replicated so that I can use it as a base to restore SQL.  So far the testing has worked ok.  What I'm trying to learn is the best way to restore the cluster to the standalone server and have it look the same to the affected app servers.  

The cluster has several instances.  In my testing, I've recreated the instances, but I don't think they show up as they do on the cluster.  For example, if the Windows server name is SQL01, and I install an instance called SQL-APP, SELECT @@servername while connected to the instance still shows SQL01 but in production it shows SQL-APP. What do I need to do to get everything to match up?  I suspect that, while I haven't seen any problems, there could be something I'm missing that would manifest itself later. 

Also, in testing, am I better off to delete the cluster server account from AD and join the domain with the DR server under the same name?  (this is an isolated bubble so no impact on production).For the purpose of this scenario, assume all other required servers (DC, DNS, application, etc.) are present in the test environment as they would be in production and nothing requires resources outside the bubble.  The only item affected is the SQL cluster.