You can choose an image from among the photos that you have already uploaded, or you can get creative and upload your own. Perhaps you would like to use one of mine?
Here's an example...
I have added over 225 FREE images to my gallery sized for use as Facebook Cover Images. I repeat, these are FREE for personal use. You don't need to be a Member or ask me for permission. I only ask that you include a link back to the original (or just to http://digitalblasphemy.com/) when you use one. I haven't adorned these with massive watermarks so please share my link!
Here's what my own profile looks like using "A New Dawn"...
Where can you download them? You can browse them all directly staring here. Otherwise, if you see a wallpaper you like in my gallery then look for the 850 x 315 link under the "Free Mobile Wallpaper" links. Download it to your own computer or device and then upload to Facebook as you would any other picture file.
The link looks like this:
Here are five more to get you started and you can browse the whole collection here.
"The Eye of Aquila (2012)"
"Starburst (Happy Independence Day!) (2013)"Let me know if you have any questions or comments!