We are trying to add a custom domain that integrates an Akamai edge hostname which we have already setup with our Azure App Service. The goal here is this mappping :
site.com -> site.com.edgekey.net -> site.azurewebsites.net
However in the App Service custom domain blade you can only go from :
site.com -> site.azurewebsites.net.
There is no way I can see that you can add the Akamai edge hostname. I've looked at the Azure CDN option but that only allows you to purchase CDN service from Azure, then integrate that into your App Service.
Is there a way to integrate an Akamai edge hostname into an Azure App Service custom domain?
As you know, we can add a root domain contoso.com or a subdomain www.contoso.com or a wildcard domain *.contoso.comin in the custom domain of web app service. You could follow this tutorial: Map an existing custom DNS name to Azure App Service
However, in this case, if you have custom domain site.com to the custom domain of web app service, you can add its subdomain sub1.site.com to the hostname. If you want to map site.com.edgekey.net -> site.azurewebsites.net you at least need a domain com.edgekey.net, then you can use a CNAME record name site in such domain com.edgekey.net to your web app service. I think it's impossible as the domain com.edgekey.net is not compatible.
If you want to use Azure CDN, Azure CDN support to add your custom domain to Azure CDN endpoint. You could view the details here. Let me know if you have any question.