To enable DNS resolution for AWS resources from GCP after establishing a VPN connection between them, you can set up DNS forwarding between AWS and GCP. This allows instances in GCP to resolve private AWS domain names and vice versa.

Please refer to the following official documentation to set this up (VPN is a prerequisite for this configuration):

GCP to AWS DNS Forwarding using Cloud DNS: https://cloud.google.com/dns/docs/zones/forwarding-zones

AWS Route 53 Resolver DNS Forwarding:
https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/resolver.html

These links will help you configure a bi-directional DNS resolution setup between your AWS and GCP environments.