You can publish your Web Store under your very own domain.
Go to Settings -> Domain on the left pane of the Dashboard:
You can set up your own custom domain in Domain settings
You can set up your CNAME Records: just choose appropriate option and the settings will be shown.
AWS (our servers) sometimes have troubles with validating certificates.
If there is no CAA records then add new CAA record as on the images: with - Only allow specific hostnames (instead od Name "pay" put in your subdomain or @ if it's root domain):
