A plausible explanation of Annabelle's identity would be that Kate may have Dissociative Identity Disorder – a condition previously known as Multiple Personality Disorder. DID is a mental disorder that involves a disconnection between a person's thoughts, memories, identity, emotions, perceptions, behaviour, and sense of self. According to American Psychiatric Association, the dissociation is associated with the coping mechanism to deal with "traumatic experiences such as an accident, disaster, or crime victimization" that might otherwise be too difficult to come to terms with. The person experiencing it may "dissociate the memory of the place, circumstances, or feelings about the overwhelming event, mentally escaping from the fear, pain, and horror," which may very well make it a challenge to remember the specifics of the experience later.
We've seen Kate grapple with placing Annabelle in her memories, and it's no doubt that she's endured an inundated amount of trauma in her life. Could Annabelle be her way of displacing those harrowing memories with a version that's more comforting to her? Reddit user Kareberr86 accredits Kate's gap in memory to this theory. It sure has legs.
Another Twitter user noted that '95 Kate's personality "switches from sweet and sensitive to ruthless and mean." And that Annabelle is Kate's other, meaner personality. That'd put her fireside story in so much perspective.