Your computer desktop is also a public space - especially if you ever do presentations or simply have colleagues look over your shoulder.
So get rid of that wallpaper showing you at the beach...really, the best wallpaper is none. Murphy's law rules: you'll have to exit PowerPoint for some reason when the SVP is watching, and that photo won't convey what you want it to.
Same for clutter. If your desktop is covered in icons, it's like having paper scattered all over your desk. Executives notice this. The fix is easy: put all those icons in a folder on your desktop. When you're working, leave the folder open and it's just like having your icons all over your desktop. You can close the folder when you present.
A neat, clean desktop and simple wallpaper will signal that you mean business.
Use your personal machine for funky wallpaper. (You do have your own computer, right? Keeping personal files and photos on company hardware is not a good idea. It's their property, and you could lose access to it with no notice. Not to mention the implications of having anything questionable on company hard drives...)