How to change the background color of the sub menu in Neve
The drop-down menu available in the Neve header builder with the Primary Menu component inherits its background-color from the header row.
If you want to set a different background-color just for the drop-down menu, just add the following color into the Additional CSS editor within the Customizer.
.nav-menu-primary .sub-menu { background-color: #91ce78 !important; }
A color picker that generates the hex value is available on this page.