Jo Ann, you might want to grow them side by side. Petite Monet does not appear to have the distinct burgundy and the base of the standards and on the hafts that your iris has. I really like your little guy, but so far have not been able to find any other possibilities. It's beautiful just the way it is! Good Luck!
They do grow side be side.
I dug them at a local iris farm ages ago.They never did well until this year.The first one just exploded with blooms ,Petite Money had two stalks.
This is a photo from a week ago.
When I said you might want to grow them side by side I meant if you really want to check for the name you could look for a rhizome of Petite Monet from a reliable source and plant it next to your 'Petite Monet/Noid' iris. Then when they bloom you can compare them. I just wrote about this process on another thread...I'll look for the link.
I do think the other iris looks like Swerti. You can check that ID by the same method if you want. I know several members grow Swerti so you could probably get a piece easily.