The correct approach involves creating a Cloud DNS zone with private visibility and associating it with your VPC to register internal DNS records for each instance. This method aligns with Google's recommendations by leveraging Cloud DNS for internal service discovery without the need for external DNS servers or unnecessary VPC configurations. Custom hostnames do not fulfill the requirement for a custom DNS zone. Deploying a BIND DNS server, while possible, is not recommended as Cloud DNS provides the necessary functionality. Creating a new VPC and configuring two DNS zones is overly complex and does not facilitate communication between VPCs without peering.