Your theme controls your site's background color, and Shogun does not offer the option to change this.
You could try to override the theme given selection, but please note that this is not supported by Shogun and if this does not work for your particular needs, we would recommend contacting your theme developer.
There are two methods of achieving this - inside a Shogun HTML element for a single page, or in your theme for your entire site (contact your theme developer for more information).
For your theme's CSS files, you will need the following code.
body { background-color: #your-hex-color; }
For the HTML Element option, you will need to modify this slightly, as follows,
<style> body { background-color: #your-hex-color; } </style>