The Divi Theme allows you to add background images to Divi Builder sections, rows and modules. By default, Divi doesn't allow shortcodes in the background image URL field. If you want to use a shortcode to generate your background image URL (or part of it), here's how to do it.

Adding a Background Image by Shortcode using Divi Shortcode Enabler

Divi Shortcode Enabler lets you use shortcodes in various places where Divi does not normally run them. As of Divi Shortcode Enabler v1.0.9, it supports shortcodes in the background image URL of Divi Builder elements. You can use it like so:

1) Enable Divi Shortcode Enabler.
2) Open the settings for the element (section, etc.) you want to add the background image to.
3) Click on the "Add Background Image" as shown:

4) Click "Insert from URL" and enter the shortcode which generates your background image URL. You can also use a shortcode to generate just part of the URL, as shown here:

5) Click "Insert into Post"
6) Save the Divi Builder element settings, and then save the page.
7) View the page on the front end and you should now see the background image generated by your shortcode. Note that the background image doesn't (yet) display in the Visual Builder preview.