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
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Create a theme from existing website
I've updated the Zulip link in both places I found it. No need to post again, unless you have something new to say. We'll pull together feedback from all the sources.
Backdrop CMS Core Priorities
Should we post here again, what we posted over there? Or would that unnecessarily duplicate things? The link to a Zulip thread in this initial post leads to an internal one, but there's...
Backdrop CMS Core Priorities