And from home after checking it out, just to clarify the details for others:
Dunno how this works for any other share selections, but for 720 or 1080 iDevice share, once it is selected, click the "Settings" button, and where it sez "when done", click the default "Library" for a drop-down menu. At the top of that menu, select "do nothing". When you then click "Next" in the lower right, it will bring up a box with the default filename giving you a chance to change the file name and select where you wish to save the file. (Remember that the "v" next to the file name opens up the folders for the "Where" that has been selected.)
Hope this helps any other random seekers. Can't say I found it intuitive, but it must have been easy the first time I did it years ago on my iMac. When looking at the choices on my MB while away from my iMac, I failed to see the "do nothing" option at the top.
Oh. I see Tom beat me to this information by 3 minutes, using fewer words..