@jconway Documents can be hidden (Document Visibility) and field data can be hidden but you cannot restrict a Recipient within an envelope from seeing the other Recipients of the envelope either through the Inbox of their account or via the completion notification.
Personally I would consider any hidden details, especially Recipients, a liability to a document if others are signing that document but I could see circumstances where anonymity is beneficial.
Here is an option. Set up either a Signing Group or use alias emails for the Recipients. We often use email aliases such as “approvals@domain.edu” (generic example) and then those individuals who need to approve are allowed access to that email inbox and remain anonymous. (Note: They still sign a Name to the signature but the email is somewhat masked). Signing Groups can contain multiple Users and go to a central email address. (same signature issue applies).