"The Ghost"

The "Ghost" is a vigilante crimefighter in Gotham City.

Post-Arkham Knight Incident
After Scarecrow revealed Batman's identity to the world at Arkham Asylum, Bruce Wayne and Alfred Pennyworth seemingly perished in an explosion that destroyed Wayne Manor as part of the Knightfall Protocol. Later, as a group of thugs attempted to rob a wealthy family (mirroring Batman's backstory), they were stopped by an almost demonic and monstrous being resembling Batman.

Arkham Episode Incidents
When Catwoman sought out the Riddler and Robin arrested Two-Face, the master criminals' lackeys talked about a ghost that had been stopping crimes around Gotham.

Equipment

 * Fear Toxin (unconfirmed): During the first sighting of the "Ghost" by thugs in the middle of a robbery, the "Ghost" seems to bring about the effects of Scarecrow's toxin in order to terrify his victims before gliding in on them. It can be assumed that if the "Ghost" is indeed Bruce, he had somehow replicated the improved fear gas and put it to use, though as mentioned before if it is the fear gas, along with who the "Ghost" is hasn't been confirmed.

Trivia

 * The appearance of the "Ghost" was possibly foreshadowed in Arkham Origins during the Joker's POV sequences, though his version of a monstrously demonic Batman was noticeably different from what appeared in Arkham Knight.
 * Its identity is not certain but it is implied and speculated by many that Bruce simply adapted another identity for himself by becoming a full-time vigilante; its appearance perfectly matches the hallucination Scarecrow witnessed before his arrest.
 * In a Reddit AMA, Sefton Hill wrote in regards to Arkham Knight, "I liked the very end! When Batman is left with no other option, he still manages to find a way out. To become an even more badass version of Batman. How cool is that?" which suggests Batman did indeed fake his death and returned a stronger, darker Batman as the "Ghost".
 * If Penguin is turned in after Batman’s identity is revealed, during the Batmobile ride back to the GCPD Building, Bruce is questioned as to what costume he will wear next since everyone knows he is Batman, mockingly suggesting a squirrel; Bruce responds with “You’ll see.” This implies that despite the Knightfall Protocol, he still has some kind of persona-based plan for when his time as Batman comes to an end.
 * The "Ghost" remains unnamed but several thugs use this name to describe the nightmarish creature.
 * If the creature indeed is Bruce, the nickname is fitting as in some continuities he was a fan of and inspired by Simon Trent, the hero known as the Gray Ghost.
 * The "Ghost" is named Nightmare Batman in the concept art gallery, though it is never called this in the Arkham Episodes set after the events of Arkham Knight.
 * A mod for the PC version of the game allows what could be assumed as the "Ghost" to become a playable skin, giving the clearest view of what the fear gas-induced hallucination of Batman and possibly the "Ghost" looked like.