Google is sending out a new notifications via the Google Search Console when the AMP viewer search shows the AMP's hostname in the header from the wrong domain. Google's John Mueller said on Twitter "if you're using a CDN, use a CNAME with your domain name so it looks sane." "We're sending out notifications to sites that have this "wrong" (eg [random].amazonaws.com )," John added.
Here are his tweets:
@JohnMu We're sending out notifications to sites that have this "wrong" (eg [random].amazonaws.com ), let me know if you have any questions!— John ☆.o(≧▽≦)o.☆ (@JohnMu) March 6, 2017
So if you are not using Google to host your AMP content but AWS or another CDN, you can CNAME the AMP viewer URL to your own domain name so it looks better:
John said if you have questions, hit him up on Twitter with those questions.
I have yet to see a notification or complaint of a notification about this. As I do, I'll add a screenshot here.
Forum discussion at Twitter.