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I've read in a few quality sources that image file names can impact keywords rankings.
If an image is called 123123.jpg for quite a while and this image is indexed by Google. Now, I would like to change the image name to widget-keyword.jpg. Do you reckon that this may create Google broken links or hurt me in any other way?
I don't know if that has any effect on the rankings of the page that the photo/s are on, but I suspect so provided there's clickthrough traffic with the images that come up in searches for the image-keywords you are targeting. I also didn't change them all in a short time, but did it over an extended period of time too
will changing the image file names cause broken links in any way in Google?
They'll simply delete the old files with the re-named ones.
Does this actually help with SEO?
Yep, sure does.
Any research was done that supports this?
Yep, my experience:-) Just think of it this way.
You are SEOing for widget just like many other people however some people actually call it widgetX. Are you going to proud and say it should only be called widget or are you going to include synonyms widgetX, widgetY and widgetZ and give the SERPs and a potential user the chance to see your site?
I get thousands of referrals every month through synonyms, ignore them at your peril.