The background color of a WordPress site can be changed by modifying the CSS.

Note: Before making any changes to a WordPress theme, add a child theme.

Log in to your WordPress admin area.

Go to Appearance > Editor.

Enter the CSS to change the background color. Below is sample code:

           .site {
              background-color: #XXXXXX;
           }            

.site is the css class for the whole site.

XXXXXX is the hex code for the color you want to use.

Click Update File.