If you need to use images that are well known (or at least are searchable online) you can mess up the way Google recognize the images by doing small changes to the images. You need to destroy the patterns that make the image easy to associate.
For example, with face recognition or pictures that are already online:
- You can change the background color and use a color that will
"merge" the image of the subject with it
- AND then you also do a flip horizontal and add an angle to the image.
This is an example of an original, Google recognize it instantly:
This is the result on Google image search of the original image:
This is a modified version:
This is the result on Google image search of the modified image:
You have no choice in doing something like this since your issue is not the indexing; your issue is probably that other sites have the image indexed and people can save your image and do a reverse search of it (If I understood the question well.)
Make some tests, flip the image, rotate a bit, add a pattern to the background, etc. You'll find a formula that works for you. My example is a crude one!
Barack Obama example
Search result of modified: