For those wondering where the option to change the viewport Background Colour went in Daz Studio 4.7, it’s now over on the other side of the screen, in Window | Style | Customize Colours…
Don’t choose the top “Background Colour” option (that changes the User Interface colours), but choose the bottom colour named “Viewport Colour”…
However, even that won’t do the trick. What will actually show up at the back of the render is set in the Environment Pane, found via Window | Panes (Tabs) | Environment. There you can set a solid color or a backdrop picture…
While you’re wrestling with settings, you can also get rid of the hideous ‘orange flashing’ on a new install, which blasts your eyes every time the cursor passes over a model…
Update: at 2020 this setting is now found in: Draw Settings | All.
Then switch this drop-down to Bounding Box only…