Google said that it is okay and even normal to have the same image placed on more than one page on your web site. This implies it does not hurt your rankings in Google to share an image, even if the image file name is different but the image is the same, on multiple pages throughout your web site.
John Mueller from Google responded to the question on Twitter that asked ” If I have 1 picture which is displayed on 2 product pages (it’s the same object on two different products), is there a problem to declare it on the both pages with my sitemap.xml?” John said “Not a problem – that’s fairly common.”
I do it here fairly often, and I don’t always use the same file name for the image I use. Sometimes, either by accident, for convenience or on purpose, I will upload the same image to my server, which creates a new image file name. Then reference that same image, with a different file name, on a different post. Sometimes I use the same filename, sometimes I don’t. I never thought there would be an SEO issue with this and John is basically saying that.
I guess it might be an issue if you want your images to rank well in Google search. Then having one image, that is always referenced, is probably a good idea. This way you consolidate all signals to that single image?
Forum discussion at Twitter.