I don't know if you have the option in the app to switch between continuous naming and resetting to "DJI_0001" every time a new and empty card is put in the drone but one other thing will trigger reseting the counter and that is shooting the next image (photo or video) after DJI_0999.xyz. (I believe the threshold to be 999).
The 999 + 1 image goes in a new folder on the card, probably "101Media" in DCIM.
I do not think this can be changed. So, if you store all you photos from the drone in one folder on your PC you will have to rename them after they are on the PC. That is if you want to avoid duplicated names.
You can use something like Bulk Rename Utility to do this.
We're all going to have to go and test it now !
Design rule for Camera File system - Wikipedia has the standard I was talking about, and it seems I was wrong about the 500 files in a directory rule, and the files can go up 9999 in the same directory. Splitting before that is left to the camera maker, and it seems to be the number of files on my cameras which trip it: if I shoot 0000-0498 and delete 50 photos, picture 0549 will be the one which rolls over.
The directory should be a 3 digit number followed by 5 letters of the maker's choosing, so if the first is 100Media the next is 101Media and so on. Some makers base the 5 letters on their name, others use generic names. Lot's of rename tools exist.
I always rename any files I intend to keep with something relevant to the picture or video so it makes no deference what number the camera gives it.
I did that to begin with, now I try to keep the sequential number in the file, set long titles and keywords in the Exif data. I couldn't remember names of 5 year old photos, if I want to find that picture of a on holiday was it "ClownFish-Feb-09-40" or "Nemo-102" so I just type in the search box and get possible matches. I've probably put "Found Nemo!" in the title and the "Clown Fish" in the tags, along with "Ocean" and a broad label for where it was.
It should stay the same, the problem arises is if you had a higher number image on the later card, it then takes its numbering from that image
For extra clarity - if you had a high number image file, which matches the camera's naming scheme and is in the right directory. I've completely loused things up by moving cards between two cameras by the same maker. The one which was behind lept forward by a few thousand and both cameras were creating identically named files.
Fortunately now the cameras let me set the prefix before the numbers, so I've worked through IMG1xxxx IMG2xxxx and now I'm on IM11xxxx, IM12xxxx etc
Once the drone gets past 10,000 I will have to start doing a bulk rename and change DJI_xxxx to DJI1xxxx