Our data partner, CellarTracker, uses distinctions between private/public notes a bit differently then you might.
All tasting notes should go in the Public field. Whether they can be viewed or have your name associated with them is a setting that can be changed via CellarTracker, in My Account → Privacy Settings.
As for the Private note field…. Suggested use for this is a comment such as who you drank the wine with, etc. This field is private.