If this is your personally-created, copyrighted, image, Jon, then yes, you have a right to ask other people not to use it without your permission. If, however, you do not hold the copyright to the image, then anyone else has just as great a right to use it as you do.
The best way to ensure a unique avatar is to create one yourself. That way it's your property, and you can be sure that you are the only person who will use it.
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