"D. Gibbons" is a name featured on one of the notes seen on the Mosaic Investigation wall in Mark's flashforward. As one of Mark's few initial solid memories of the flashback, D. Gibbons quickly became a key character for the Mosaic Investigation.
When a woman named Didi Gibbons first visited agents Benford and Noh the question arose if she could be the D. Gibbons. However, it was soon revealed that Didi's involvement with the GBO wasn't direct, but rather linked to a man who had been conscious during the blackout, and also had cloned Didi's credit card.
Not much later though, the - presumably - right "D. Gibbons" was mentioned by agent Benford's daughter, Charlie, who, when prompted by Benford to tell him what she had seen in her flashforward, stated: "D. Gibbons is a bad man."
In Mark's flash forward there was an FBI subject case file for one "Deacon Gibbons", to which the "D. Gibbons" note was attached. According to the file, Deacon Gibbons was wanted "in connection to a murder of a Salt Lake City police detective" at Divine Doll Company, as well as in connection to "the flash forward event". However, following his wakeup from the GBO, Mark has not shown any signs of remembering the case file.