Hi,
You will need to create your Private DNS Zone without my-database. This should be your name: private.postgres.database.azure.com
resource dnsZone 'Microsoft.Network/privateDnsZones@2020-06-01' = {
name: 'private.postgres.database.azure.com'
location: 'global'
DB server name should be your A record which you will need to create later.
Regards,
Karthik Srinivas