On the autogenerated page in the Orbs Registry for private orbs, it shows a "private" tag after the name of the orb.

In the next line, there is metadata such as Created, Version Published, and Releases. This line also indicates that the orb issued in < 25 orgs. However, currently orbs can only be used by one (I believe). It would make sense to hide this field (number of orgs used) in the published documentation for any private orb as it's not pertinent.