In front of the cloud an existing WordPress website

I'm afraid this might be a very stupid question, but I did some research without much luck. The Amazon documentation is not clear to me, I am missing an essential part of the puzzle here.

In a nutshell, I want to use Amazon's CloudFront with a website currently running. Website listens from mydomain.com Y www.mydomain.com.

I understand that once I enable CloudFront, I must point out mydomain.com and www.mydomain.com to the CloudFront addresses.

Problem # 1: I can not CNAME my naked domain. So probably for mydomain.com, I'm going to lose the arbitrary homing feature, right? (the www host can be CNAME only very well) Anyway, this part can be resolved with just one redirect of HTTP 301 perma.
Problem # 2: the configuration interface allows me to choose an "origin", to indicate where the server is and, if it accepts an IP address, I do not see where I specify its virtual host name (so that it accesses the IP address that passes the correspondent Host: header to match the virtual domain).

In the case of a migration, the website is normally configured in wordpress to recognize the URLs as www.mydomain.com. So if I make a new host name "hidden" as cloudshade.mydomain.com and just point CloudFront to this address, it would only get clients to be redirected to this cloud-filled host (cloudshade.mydomain.com) … If I do not do anything, what I get is a cyclical redirect: I try to access www., what queries shadow of clouds. which, in turn, redirects back to www ….

I'm sure I'm missing something stupid, because many people should already use Amazon CloudFront with WordPress websites … I guess I've just had very bad luck with Google and clicks on the Amazon documentation links.

Hoping that someone here who has experienced the same thing can shed some light into this darkness.

p.s .: I tried to remove url tags from www words without any luck, I just know there are no valid / relevant hosts / links in this post!