'If they named the party it would not be confidential." Yes it would be per following sentence.

The naming of the entity signing the confidentiality agreement is generally not part of the agreement unless the entity signing it specifically asks for their name to not be disclosed.

In other words, they have a specific reason not to be named.

I have heard of many situations where a company not only says how many, when and by whom confidentiality agreements have been signed. A partial example is recently of Noront.

In some cases even the actual reason for the agreement signed is stated.

What is not stated because covered by an agreement is what information is passed on and it's nature.