Your irises look very happy in this spot.

transplant without the rhizome?

#Clearly no.

The rhizome is the most important part of this plant. It will allow it to regrow the next year after a period of "sleep". But it is ok to transplant only a part of it if you can't dig them completely out. Here is how healthy future transplants would look like:

What is important is you wait the end of the vegetative period before you transplant them (usually end autumn). It is not necessary to dig them as deep as you found them.

Now if you see more coming the next years, propose them to neighbors, they will appreciate.

Your irises look very happy in this spot.

transplant without the rhizome?

Clearly no.

The rhizome is the most important part of this plant. It will allow it to regrow the next year after a period of "sleep". But it is ok to transplant only a part of it if you can't dig them completely out. Here is how healthy future transplants would look like:

What is important is you wait the end of the vegetative period before you transplant them (usually end autumn). It is not necessary to dig them as deep as you found them.

Now if you see more coming the next years, propose them to neighbors, they will appreciate.