Sleazy Fork is available in English.
Adds a few quality of life improvements on Sankaku Channel: Automatic image scaling, scrolling to image, thumbnail icons for loud/animated posts, muting/pausing videos, + - tag search buttons, a tag menu which allows for tagging by clicking, 'Choose/Set Parent' modes, easier duplicate tagging/flagging. Fully configurable through the Addon config.
Ah, it took me a while to get what you are asking, you mean the download button danbooru has - I never used that before, I always click on the file size.
After doing some research, it seems the answer is no, I can't implement this.
There's the download attribute for link elements, which does allow to set the file name, but Sankaku loads the image from a different domain and this feature was blocked for cross-origin domains a few years back (e.g. see https://developers.google.com/web/updates/2018/02/chrome-65-deprecations#block_cross-origin_wzxhzdk5a_download).
So the only way to implement this is on the server, which is also what Danbooru does: it adds a ?download=1 to the URL, which the server reads and the server then sends the filename you're seeing back.
You may try your luck and post your suggestion in the Sankaku Complex Development Thread.
[Feature request]
Can you implement a naming feature so Sankaku names files like Danbooru does? (*character name* (*copyright name*) drawn by *artist name* - *md5 hash*