Thank you for reaching out.
Based on your question above I understand you are using a conditional forwarder to resolve your private DNS zone entries in your ON-prem network. For your web app you have deployed a private DNS zone names privatelink.azurewebsites.net and set an A record with MyAppName with an internal IP.
Based on the documentation here Can you please confirm if you have set the DNS records as shown below?
Also, can you please confirm if you configured your set-up as described here
- On-premises network with a custom DNS solution in place
- Virtual network connected to on-premises
- DNS forwarder deployed in Azure.
- Private DNS zones privatelink.azurewebsites.net with type A record
- Private endpoint information (FQDN record name and private IP address)
Please let me know if you have any additional questions. Thank you!