This is correct - it will not show, even if you are able to see the profile of the person. The level of privacy blocks the project box's ability to display the name. When the profile is given a more open level of privacy, the name will then display.
On a side note, other project boxes have also experienced an issue if they are added to a profile and on first save they display an incorrect name. A second edit seems to fix that, even if all you do is go back and add a single space to the biography. I'm not entirely sure why this seems to happen, but at least I know how to fix it.