Several game backgrounds have been made for Pax, made by Domenico and me. The game background is the image behind the regular game screen, which you see when you are playing.
To use one of the backgrounds, rename the file from "game3.jpg" (e.g.) to "game.jpg". If there is an associated "lower_game3.jpg", rename it to "lower_game.jpg". Then, move the file (or the two files, if there are two) into your Pax Galaxia folder if on Windows, or if on Mac, right-click on Pax Galaxia.app, choose Show Package Contents from the drop-down menu, then navigate to Contents/Resources/ and put the files into the Resources folder.
You can download the backgrounds here (includes the original Pax background).