No, this is not a DID symptom. Your son might truly have some type of memory gap, but if he is in the range of ADHD, conduct disorder and similar issues, there are a bunch of other possible reasons for a memory gap involving acting out types of behavior.

It's more likely that this is not a true memory lapse, but a form of telling himself a lie often enough until he believes it as truth.

Can you tell us more about your son's symptoms, behaviors and attempts at treatment? What seems to help him feel better and/or be more stable?