We have some content hosted for our Azure application on the Azure CDN - we can access this nicely over https using the standard endpoint address, however for 'neatness' our customer would like to use a custom domain with https - so we can access our assets from https://cdn.app.com. Is this possible with the Azure CDN?
It's currently not possible to use the Azure CDN to deliver content over SSL with a custom domain name.
It would involve giving Azure access to your private key for them to propagate it to all of their sites, so I can't see them offering it anytime soon.
The closest you could get to this is if you used a traffic manager endpoint and served these from your own Azure instances. This would be more costly than running off the CDN though, and won't offer as many sites to benefit from.