I use a program called ACDSee to organize and edit pictures and other files. It used to have this feature, but doesn't in the newer versions I've gotten. It would ask you if you wanted to replace or rename, and would autofill the next sequential number for you. Now it doesn't suggest a new filename, which is beyond irritating if you are trying to put a bunch of files in the same dir. If you could find an old version of that, it can do it.
All the versions, though, have the ability to batch rename files. So you could name them random names, move them all into the same dir., sort by date and batch rename them with a sequential filename like file0001... this would most likely accomplish the same thing.
Now, if you wanted to be old school, you could write a DOS batch file that would do this, but I can't remember how you would do it exactly. If you go back in time to when I was 12, I could do it for you.