Welcome to the world of irises! From your description, it sounds like each pot holds a different cultivar (different names), but all fans in the same pot will be the same iris cultivar. A single iris rhizome will propogate itself by growing additional rhizomes (increases) along its sides. Most likely if you take a good look at the rhizomes' growth, you'll see that they're all connected to a central rz.

If the increases are large, you can cut them away from the central rz, lay them out for a couple of days in a sheltered, dry area to allow the cut wounds to heal, then plant them separately around your garden.

If the increases are substantially smaller than the central rz, leave them connected and plant the entire potfull intact.

You can find planting and culture instructions in the FAQs (link at top of forum page).

Enjoy!

Laurie