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
Worth mentioning as it was in zulip chat by @yorkshirepudding I just tested and the two work together without issue as long as you don't use the "Exclude comments from Content...
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There is also Node Comments Search - this searches the node and all comments (default search is node and first page of comments) as part of the content search. Izzy's module above is a separate...
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I have created a new module comment_search
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