Phantom, the sentient Helmet
Danny wasn't running away. He no longer had a reason to run, or to really care about his injuries (he wondered if his experience at Amity had left him numb to physical injuries, but when your father shoots you 5 times a week you start to get used to it).
The truth was that Danny was a little envious of his clone. Ellie had no responsibilities and she could travel wherever she wanted; Because of his obsession, or his mentality, Danny could never be free, he always had to stick with someone to protect. He needed to protect. It just couldn't be Amity the one he protected anymore.
Then he left his hometown. He hugged his friends and said goodbye before looking for a new "purpose", preferably one that didn't hate him. And he arrived in Gotham, with an aggressive spirit that screamed that he wanted to be protected as much as he was protecting.
It was obvious that "Red Hood" didn't know the ghostly ways, so Danny debated how to help him until he noticed his helmet, and the halfa did the only thing he could think of: he possessed it.
When Jason woke up, his helmet had developed an A.I. that he was sure it didn't have before. When he tried to restart it, the A.I. moved to his motorcycle, and well, it wasn't hard to find out that it wasn't an A.I. at all, but "Phantom" refused to leave. Jason sighed and left it like that.
At the end, Phantom turned out to be very helpful, always with reliable information, and sometimes, he didn't even behave like the A.I he was supposed to be, sometimes he was just a very tired guy, spouting vaguely worrying comments. And giving life advice to Jason, ignoring everything he was doing, like killing people (bad ones), Phantom didn't really care. Once, Phantom said that he was right, that what he was doing was right.
The first time he found out what Phantom really was was because some people cornered him, and were about to shoot him before something jumped out of his helmet. Something gigantic and vaguely threatening, but Jason felt safe. When the shadows disappeared and all that was left was a boy of his own age, clearly tired, Jason wondered if it was too late to ask him to stay out of the helmet.