So far, you have received a lot of great ideas for when you have ample space to show them all. So I won't add to that. What I *will* do is give you an idea for those times when space is more limited.
For those times, I recommend getting a good photo of each rug. Then, for when space is limited, you can either fold up (or roll up) the rugs, and use the photo as a hang tag, but also to show what the entire rug looks like. If someone wants to see the full rug, you can unfold it or unfurl it. But at least the photo would give them an idea of what it looks like.