To clarify the above, the "published names" are contained in GENI profile URL references, not in in the text of the About messages themselves. GENI obfuscates all private profile names displayed, depending on whether you have management privileges for the profile in question. Since Karen Brauer has management privileges for her private profiles, the links appear to her as the names on her profiles. They do not appear that way to anyone else.
There WAS a problem in the fact that if you were to EDIT the About section, the links also contained the names. This you can fix by removing the names and replacing them with "profiles" in the URL.
To further anonymize this, Erica Howton replaced the naked URLs with a link that used initials instead. That works fine as well but the GENI security for those profiles actually does a pretty good job already, provided the names are scrubbed from the URL itself.
This solution was presented to Mrs. Brauer but so far she is still unhappy with it and as I understand it we are in the process of deciding whether any relationship information gleaned from DNA test sites can be used without the express written permission of the testee. That would in fact impact not just GENI but pretty much the entire testing and genealogical world, so it is a rather big deal. GENI's processes for obfuscating private profiles are industry standard but apparently Mrs. Brauer's claim is that relationships between profiles may also be privileged information.