You may request at any time that a thread you started be buried in the graveyard. The graveyard is not accessible by any search engines or members (except you "Only for your threads" & staff). Also, please keep in mind that you have up to 30 days to change your thread titles before they Lock. So if you get your appraisal done within a few weeks I would suggest editing out the name(s) from the title & thread, then close the thread. Alternately you can just click the report button & ask for it to be buried to save time from editing.
Essentially your appraisal thread will only be in search for a limited time (1 day, 7 days, 20 days) till you edit or request burial, at which time it will then drop from search. Furthermore, also note that once the threads buried, even if google still has a link to the old location of the thread (normally cached for up to 7 days) that anyone visiting that link (except you "Only for your threads" or staff) will get "Sorry, but you don't have permission to view this page" error.
I hope that explains it a little better and sheds more light on what options you have to keep your names out of any long term searches.
Eric Lyon