Hi again!
If you don't intend to trade Irises, and only have them for your own enjoyment, it doesn't matter if you know what their names are, etc. However, if you think that you might enjoy trading, or gifting Irises, and you know the identity of the Irises that you have, then it's a good idea to remember what is what. And as your Iris collection grows, that gets harder and harder. Most of us have some kind of plant identification system. I like the plant markers offered by Kinkade Gardens -- they're metal and durable and hard to dislodge. I also keep a database of my Irises, listed alphabetically, with date of acquisition, where I got it, who the hybridizer is, the color of the bloom, the location of the Iris here in my gardens, and a photo reference. I also have a map of my main Iris bed showing the location of each cultivar. If you're thinking this is a little obsessive/compulsive -- it is. You don't have to do any of it, or you can do some of it.
As far as the Iris that you bought that is identified on it's container -- that's probably good enough authentification. If it blooms differently, though -- then you've got some detective work to do. Every now and then, even a conscientious grower and seller will mis-ship -- mistakes happen.