When exporting slices in Photoshop through the Save For Web... dialog, PS automatically names as the
.png. So for example:
It is also possible to manually input a filename for a slice; which will then override this numbering system. My question is: how can I get rid of this slice name? I want to revert to the default numbering behavior. Deleting the "name" field in the dialog has no effect (it simply resets to the last used name).
The only workaround I have found is to delete and recreate the slice, which is terrible.
Photoshop's Save for Web & Devices tool actually offers multitude of options to control slice file naming, and you don't have to reset the slice name itself. Instead, you'll want the slice file name to include the slice number instead of the slice name (you have given). On CS5 and newer, to control this, after pushing the Save button in the Save for Web & Devices window, before pushing Save again, find the Settings dropdown menu and select Other...
This opens a new window to control all the saving options and give the slice files names consisting of e.g. document name, slice name, slice number, current date, custom text, and any combination of these.
For your case, the correct answer would be to make the File Naming section to consist of doc. name + underscore + slice no. (01, 02, 03 ...) + ext. to give the slice file a name of mydocument_01.png, for instance.