The <private> label in the family tree is shown for living members when guests visit your family site. That way, you can display your family tree to others whom you don't know (but who might have genealogy information about your family) without compromising privacy.
If you are seeing the <private> label after you are already logged on, it may be there is a problem. One way to check this is to log off and look at the tree as a guest and then log back on and visit the tree again, this time as a member.
One reason you may be seeing the <private> label as a member is when a family tree was created in a language other than English and then posted to a family site.
In order to correct this error, all that must be done is to translate the names in the family tree using Family Tree Builder.
The Translation Wizard under the Tools menu will help you do this seamlessly. It will automatically translate most common names from a specific language into English. Any untranslated names can be changed manually by you after the wizard has done its job.
After completing this step, all that is left to do is save and re-publish your tree to your family site.
Give it a try and let me know if you run into any obstacles.