although being able to get this information would make it relatively easy – or at least easier – to sync up your personal photo collection with your iNat observations (there are third-party tools like naturtag that try to do stuff stuff like this), the only the place the original filenames are available to regular users is on the photo pages (which you would have to then scrape to get that information).
there was a request to make the information available in the in API via a new photos detail endpoint, but that hasn’t gone anywhere.
however, it looks like someone has actually done some coding to make original filename available in the API via observation details, but i don’t think it’s been completed yet (although it might be done sooner than later).