Sure, just rename the photos.
In the library module select all photos you want renamed, go to Library > Rename Photos... (or just press F2)
In the dialog box that appears select Edit... (the bottom option)
and in the edit box of the next dialog paste this:
If you have more than one photo in a given second, LR will append -n (where n is 1, 2, 3...) to the filename.
Thats what I thought but it did not work. After a reboot it worked!