Im trying to access this variable but I'm getting a null value, {{ site_name }} page.html.twig
Drupal suggest that I check the theme settings and enable this display.
* - site_name: The name of the site. This is empty when displaying the site
* name has been disabled in the theme settings.
However when I check my themes settings I don't see anything useful http://puu.sh/lOqTY/97a7a12ae8.png
I also checked the global settings, http://puu.sh/lOr0S/0ed321e23e.png
In my case I was calling site_name variable from the twig template of Site branding block. I was also suffering for site_name was an empty string.
Than I found Site Branding block settings at Administration > Structure Block > layout > Site Branding. There you will see "Toggle branding elements" tab which allows you to show / hide the site name, logo and site slogan.
Check if you have Site name marked to be shown. Than save block settings and clear the cache. site_name should now work.