I believe the following will work for you.

nav.user-menu-navigation {

background-color: red;

}

Obviously replace RED with the hex color you want.

That did work, thank you! 

@dgladfelter you wouldn’t happen to have the CSS for changing the text color for the user menu too would you?

Menu text would be:

.user-menu-item-title {

color: aqua;

}

The active menu text was a bit trickier to get to work on my end. I had to do:

doc-layout-user-menu .user-menu-item.user-menu-item-active .user-menu-item-title {

color: red;

}

Hmm, I tried both options and neither seemed to change the menu text color.