The digital camera I'm using (Olympus Stylus) automatically gives each picture it takes a name.  The name starts with a letter and then has a 6 or 7 digit number that seeming increments for each new picture taken.  Sounds good so far...
  I've never seen any kind of problem/issue related to the uniqueness of the filenames.  That is, I assumed they were unique and I never had any reason to believe otherwise.
  Yesterday I learned that my camera has a nasty habit of reusing filenames!!!!  That's right.  If you copy some pictures off the camera and then delete them from the camera, the camera may use those filenames again when it takes new pictures!!!!!  Horrible!!
  My whole family uses the camera, and every once in a while I'll remove the fig pictures I've taken.  I'll just dump them to a directory on the computer and delete them from the camera.  Then we'll all take more pictures, and some time later I'll dump my new fig pictures to the same directory.  I don't always take them all off, and I don't always delete them, so it is not uncommon for me to download pictures from the camera that I've already downloaded.  I got used to that "filename already exists" dialog box where I either abort the copy or just copy over the image.
  However, I just realized that I overwrote a whole bunch of images I took throughout last summer because new pictures were created using the old filenames.  Arghh!!!!!
  Beware!  Your camera may have the same awful feature!
Jim

Dang.. that's awful. I been using my smart phone for the past few years and it uses a timestamp for the filename. No problems there.

My phone goes up to 999 and then starts over. It will not start over until it has reached 999 though. I always presumed my camera did the same.

After uploading pictures to computer right click picture and change the name .
Here is example used to related to what is being seen in picture.

File name changed from what camera originally used  and renamed to - Cold Morning.jpg
as it was about 18 below zero.

Many camera's have a date feature as well to know when the shot was taken.
With figs pictures for example the type of fig cab be used in the file name followed by a number.
This is what i personally do .

I have never had that happen to me with my series of Sony, Nikon or Canon digital cameras over the years (my wife is hard on digital cameras, you won't believe what has happened to some of them).

Could you try reaching customer support and see if that is a 'feature' that can be adjusted somehow, or if it is a fault in the camera's software?  Still on warranty?

I'm not sure what model of Stylus you have but from what I've read if you go to "mode setup" and then "file name" you should have 2 options... "Auto" or "Reset". The auto mode is supposed to continue with sequential numbering. If the batteries are removed for too long or if the batteries are drained dead for too long it will go into Reset mode which will start the numbering over (unless there is a file name already on the M/C with that number assigned.)

Give that a try to see if you have that Auto mode selected.

Tyler

On Sony they go to dsc9999 and then back to dsc0001. That kind of reminds me of the score at oldie Donkey Kong II .
To avoid problems, what I do, I create a folder per download and I move all pictures every time from cameras to the pc - this way no problem .
Do you, like me,  have an Olympus as well :) ?

Tyler -- that's interesting, I'll have to check when I get home.  I doubt we ever changed it from its default, but it is very likely that we've let the batteries drain for too long.
Martin, JDSFrance -- yeah, ideally I dump them all and sort them into specific subdirectories and/or name them....but sometimes I have to just get them all off the camera, and sometimes I just need to copy a few and may or may not delete them from the camera at that time.  It is under these circumstances that this camera's "file naming feature" rears its ugly head!!!  Suppose you remove two pictures out of 100 because you need quick access to those pictures.  Then a few days later you come back and download the rest.  You run the risk of overwriting the important ones you downloaded earlier...or not downloading some new ones, depending whether you press the "OK" or "No" button on the GUI dialog box!

Terrible user interface design.  If they're going to give you a 7 digit number,  I would expect to be able to take 10 million pictures before there's a problem!

I'll report more when I look at the camera menu...
Jim