I want to paint my family room this color, but I'm having a hard time matching it up. The paint department is unable to match it up via this photo. would there a formula or a brand-color name?
This photo was posted by the photographer who is unlikely to have the paint information. Since the photo very likely is not an exact replica of the paint colour, you're best to analyze exactly what you like about the colour you're seeing on your monitor.
Perhaps the paint store will lend you a paint deck so you can take it home and hold up all the dark brown chips with your furnishings and see what looks best. Just use this picture for inspiration, but choose the paint that suits your own room.
Hope this helps.