Sorry to misuse the topic a bit:
Not misusing, it's a good question.
I have a similar question, but exactly the opposite: I am approaching 9999 on my RX10 (mk1, original). Is there a way to continue counting beyond 9999?
No, the file number rolls back to 0001 after 9999 but into a fresh folder on the card.
When you download the numbers you see will go "9998, 9999, 0001, 0002, ....".
Awkward online manual for the RX10, can't find anywhere that says that the first 3 characters can be edited like the later cameras can do.
The question from me is what do you see as your file names when you download?
On my later firmware RX100M6 I have renamed the first 3 characters so I can sort my files from my wife's if needed.
When I review the images in the camera I see on the camera's screen 100-5009, 100-5010 today for the first two on a fresh card.
When I look at the card in the notebook with FastStone Viewer or download them, I see RXA05009, RXA05010 as the two filenames. My wife's camera uses RXBxxxxx naming.
Not that I am about to experiment but I suspect that Sony might use that leading 0 so you may actually see your downloaded file name roll over from xxx09999 to xxx10001.
Obviously you will soon find out. Let us know.
I avoid any file number clashes by downloading all cameras into day dated folders and add a bit of text later, that way the rollover back to 0001 with any or all of my cameras is well separated by date, weeks, months or years apart in various cameras.
If for some strange reason I do need to gather a bunch of photos from different times then I am usually pushing those into date order in the new folder they are copied to and then renaming them with FastStone so now they would appear as 0010-RXA05009, 0020-RXA05010 etc.
The added 0010-, 0020-, etc prefix sequence allows me to later move things around or slip new images in as I find them later, that way the final sequence may be 0010, 0011, 0012, 0020, 0030, 0031, 0040, and so on. The size of that prefix is made to suit the likely number of images in the special folder, for say a TV slide show where the TV always seems to follow file name order so the numbered prefix does the job.
As for my folder dates and naming, it looks like this....
Gradually finding and adding text to all months and years that have significant trips or events in them, so "2009" later becomes "2009 Japan" and month "04" becomes "04 Japan". That way quick flicks through with any file exploring finds Japan or Taiwan or whatever I'm looking for, simple Windows searches for "Japan" also finds the folders.
I got burnt early on by a keyword type database that failed so dropped back to a totally Windows friendly and any program friendly folder naming system. I do not rename any actual file names, except extracted copies for those slide shows or whatever.
Maybe too much information, but something in there may help.