Is the "www" in the database for the site confguration? I have recently helped launch a site and there are some cross domain issues between "www.website.com" and "website.com"

I was chatting with Cloudways tech support and he mentioned that if I remove the "www" from the database for my site settings I wouldn't be having the issue.

What I ended up doing was modifying the .htaccess to redirect to "www.website.com" for now, but I still have the question: Is the "www" for the domain name in site information stored in the database? If so, would you really want to edit that?
No its not there in database.

It depends on global $base_url variable. 

How drupal define this variable is based on super global $_SERVER['HOST'] variable, which is basically depends on how the request was sent with/without www.

But you can override global $base_url in your settings.php
$base_url = 'http://yoursite.com'