This is basically a request to integrate some of the functionality of File (Field) Paths into core. Here's the file field configuration page, once the module is enabled:

The redirect and active/retractive update bit can be left for contrib (or to be solved by #854); the transliteration bit is already implemented in Backdrop (admin/config/media/file-system); the redirect can be left for a separate issue (or contrib); what I find a valuable feature though is the ability to use tokens for file names and file paths. The later is what this issue here is about.
Original request
There is a feature request for this filed in the File (Field) Paths module issue queue that is marked as "closed/fixed". It states that Entity API exposes this as a token (I think it's the Entity Token sub-module actually):

Looking at our token browser though, the deepest I could get to is [node:field_image].
Recent comments
@yorkshirepudding thank you for the additional info on improving discoverability and a handy way to keep a list of projects for reuse.
Why not add a Github star?
It is a good point @izmeez and when I was researching repo discoverability I found that GitHub search does prioritise matches with more stars. This is what I was researching for:...
Why not add a Github star?
Do you have a separate development environment and transfer database and config between sites?
Wierd happenings regarding updates...