Barbara

Who?
Jack mentions Barbara, quite often to AMs. We don't know who Barbara is or Barbara is a metaphor for something else.

Important Stuff to Know
During Season 3 AM Kim (Detective Stewart) received texts from Jack with lyrics. Kim was able to figure out that the lyrics were from Regina Spektor's Chemo Limo. In the song, Barbara, looks a lot like the mother's mom (so, Barbara's grandmother). Barbara could symbolize a child that has been forced to grow up fast due to the stressful situation of having a mother with terminal stage cancer.

Per Dex, Barbara is not his mother.

Evan, an AM, is called Barbara by Jack.

In Rehearsal (the NF Sept show) Dex let's you bare witness to a dream sequence. One of them includes Jack being interrogated by a Detective (the participant is in Jack's lawyer's shoes). During the interrogation Jack says that he received a private phone call, the caller said "Put your hands up, Barbara" and his husband screaming.
 * Jack was formerly married to an astronomer
 * They lived in San Francisco together
 * They had a dog named Gyarados (yes, that's a Pokemon)
 * The husband was brutally mutilated but no blood was found at the scene. There was one cooked egg on the stove.
 * The detective strongly suspected Jack being the murderer (Jack vehemently denied all of this)