Help our customers to whitelable our application without opening the TCL and UDL to the world

We are having our application deployed on AWS at the moment and all the ports for incoming are closed and restricted to only the server IPs as a security measure. We should work around to securely allow the following redirect or whitelableing process.

For example my application is Subdomainname.mycompany.com ; Customer map in his domain setting with a CNAME record to direct from his website either A or CNAME record customerdomain.com or Sub.customerdomain.com to our application Subdomainname.mycompany.com

We are looking for an expert combination of AWS AZURE and .NET as we are currently hosting on AWS and will be migrating to Azure in a month or two.