Is Cover Sheet Necessary for Writing Letter Submission?
I did my application for grad school pre-internet, and no writing samples were requested.  So this is not intended as an authoritative answer.

The instructions you posted weren't super clear, so I compared them against another randomly chosen program.  It happens to be for an MFA program: http://english.olemiss.edu/how-to-apply-to-m-f-a/


  Please provide a cover sheet with your name, address, phone number, and email, and the titles of the pieces in your work sample.


Okay, now I'll extrapolate from that and make my best guess.  (If you don't mind waiting until Monday to do your submitting, you could ask the departments for clarification.)

Program A: If your pieces of writing already have your name clearly indicated somewhere near the top of the first page, then perhaps you don't need to add anything; however, a cover sheet as requested by the MFA program I quoted might not be a bad thing.  If they find it extraneous, I suppose they could just toss it.

Program B: If the piece of writing is not published, I would guess this means that you should add the name of the program you're applying to below title and author, at the top of the page.  If the piece of writing is a reprint of a published article, then my personal guess about this would be to use a pdf editing tool (e.g. Foxit's "typewriter tool" or "textbox").  If you are not the sole author, then in addition to the name of the program you're applying to, it might be helpful to put your name in that textbox too.

I guess if the reprint doesn't have enough space at the top for such a textbox, you could make a separate cover sheet, and then splice the two pdf's together with for example PDF Splice &amp; Merge.

A nice extra feature for non-published pieces of writing would be a header or footer with your name and the name of the program you're applying to (and page#/#pages).  In case the committee is sitting around a table with hard copies of applications, and things start to get messy.  (I have no idea if that's how some committees work.)