Availability Group Clustering - Cluster Group Preferred Owner We have a three node AG. Two nodes in a local data center, one in a different subnet DR site.  Am I correct that the Cluster Name should have two IPs, just like the listener? 

Also, is there a way to set the preferred owners of the Cluster Name and Witness so it won't try to fail over to the DR site if the primary nodes are up? 

Additional Info: We had an outage from patching a secondary node, we couldn't figure out why a secondary rebooting caused the AG &amp; Cluster to go down.  We opened a support ticket with Microsoft and they recommended we change the possible owners of the Cluster Group to exclude DR.  So what appears to have happened is the Cluster Group tried to fail over to the DR site, it couldn't come online because there was no subnet IP. That took just long enough that quorum was lost because the witness didn't come online, and the secondary was rebooting.
Yes, you need to add a DR site IP address for the cluster name.  It may not be critical if you aren't using the cluster name for anything, but it is certainly a best practice and considered the correct configuration.

You don't really need to be concerned about the core cluster resources (cluster name, fileshare witness, etc.) failing over to the DR site.  The cluster will run just fine if that occurs, and if the network to the DR site is interrupted, the two nodes in the local data center will arbitrate for ownership of the core resources and one will bring them online.  This will not cause the availability groups to go offline and come back online--that will only occur if the AG primary can't retain ownership of the AG resources.

Having said that, you can set the possible owners of the cluster name resource on the Advanced tab, but in the case where you need to fail over to the DR node, you would need to change it again in order for the resources to come online on the DR node.