Applying to Teaching Position in the Same Department as My Advisor... Should I Mention Her? I'm applying for tenure-track teaching positions right now and have, more or less, a single cover letter that I modify for each one of my applications.  

It so happens that the department my advisor teaches in has such a position and I am intending to apply.  To give some context to this, my graduate program was at an institution that is associated to but very distinct from the institution my advisor is a faculty member of.  Though my PhD advisor is one of my biggest professional connections, I hardly have any other connections within this department, though most other people there know that I was her PhD student and would certainly recognize my name from my application.


  My question is: Is it necessary/recommended that I modify my cover letter to reflect my relationship with my advisor in any way?  If so, what should be included?  


I honestly think there is a slim chance I would be selected for an interview let alone hired, but I would like to get a sense of what's appropriate in this kind of situation.
I would mention her, certainly. You don't need to make a big deal of it, but just mention somewhere that you worked on your dissertation under the guidance of Prof M. It is probably a matter of public record in any case. 

You should also probably give her a note that you are applying to her department. Under the circumstances you state there should be no issue about it, and she may be able to help you along if your relationship was good. Being at the same place gives you a way to carry on research trajectories already set in motion. 

She probably won't do for a formal letter of recommendation, however. 

And you can, of course, ask her before you apply about the advisability of it and also this very question.