Additional SQL Server features and topics not covered by specific categories
Figured out the issue. Update-AzSqlVm takes a name as a parameter. This name is the VM name and has no relevance outside of being the resource name. I'm sure it's pertinent to the IaaS agent but internal to Windows it is meaningless. When adding the second node to the cluster, it is trying to use the VM name instead of computer name and thus failing to find it. I suppose MS expects people to either name the VM and Computer the same or add the VM name to DNS. Neither of these options is favorable and it really seems like this is a huge bug in Update-AzSqlVm.