Ordinarily, it is a good idea when transplanting Irises to cut off the leaves in a fan-shape. This allows the rhizome to concentrate its energy into developing a root system, rather than spend energy trying to maintain those leaves. You know that your rhizome has *settled in* -- when it begins to form a new leaf in the center of the fan. This is humorously referred to as *getting the finger*!!!
The bent-over leaves on yours are an indication that the rhizome doesn't have the resources to maintain full leaf-length. Watering would help, as Leslie said. You could still cut the leaves (leave about 6" of leaves) into a fan. And the drying off of the outside leaves is normal, as has already been mentioned.
You mentioned adding compost to your soil -- I would be very careful about that. Compost has a tendency to hold water and Irises don't like *wet feet*.
I think it's exciting that you don't know what Irises you have -- that's like waiting for Christmas!! I look forward to seeing your pictures when they're in bloom!!!
