I cannot tell you how tiresome it was to try to correct people who assigned me the same last name as my child's when I was dealing with him in a school setting. And you know what? I just answered to it, because I knew darn well who they were talking about. It wasn't about what they called me, it was about what was going on with my child.
Has anyone actually SHOWED you the school records that show her listed as Mary Smith instead of Mary Jones on Johnny Smith's records? To whom do you think it should be reported that she is using the wrong name, and what should be the penalty? And is it possible that she set up these files for him (say at a pediatrician's office) back when she was a Smith, and just hasn't bothered to tell them to change it? And of course, there's always the question, What difference does it make? that might be coming to the mind of everybody who hears your question. This is an ill concealed and very petty excuse for something to try to punish your ex about. "I would not mind if she got called on her misdeeds for once!" is not something you should bring up in a court proceeding. It's like, "I don't want you to have the right to claim MY name!" Well, it happened, you gave it to her once and you can't undo that. The two of you have a child together who has that name legally. She is always his mother and the kindest thing you could ever do for your son is to get along with her. You picked her to have sex with and he is the result.