Curate, connect, and discover
Danny, on the run from the GIW decides to take shelter in Gotham because if the GIW have any sense they'd never set foot in there.
Even if Batman and the JL agree with thier opinion on ecto entities (as evidenced by their lack of speaking out against the anti-ecto acts) Batman was notoriously territorial and would have issue with a wildly incompetent government organization throwing missiles around his city all willy-nilly.
With that being said it was probably best for Danny to wear a disguise. Sure, they didn't know Fenton and Phantom were the same person yet but Danny Fenton suddenly turning up in Gotham after going missing in Amity is certainly going to raise some eyebrows regardless of the necklace he had that jammed his ecto-signature and made him untrackable.
Danny started off by going blond. Its something he's always wanted to do and now with ghostly shape-shifting powers he doesn't even have to worry about frying his hair or dying his eyebrows to match. After that all he needed to do was part his hair down the middle, add a lip ring or two and maybe a bit of make up.
Danny stared at himself in the mirror. He looked like a completely different person.
A completely different and very attractive person. He looked good. The newly blond man threw on a green jacket and went out to explore the town. He did not expect to literally bump into the Tim Drake. The Wayne adoptee just stood there mouth opening and closing comically. Did he offend him? Crap. He had promised Jazz he would stay off of the radar of the Waynes and the bats specifically and here he was angering one of them.
Danny decided to book it before it became a scene, ignoring the lovestruck Tim's crys for him to wait.
Back at his apartment Danny quickly changed his look to red hair tied back into a two inch low ponytail, green eyes and freckles that unbeknownst to anyone else was made up from the lesser known constellations.
The coffee at this Cafe smelled amazing! Too bad Danny wouldn't get to try it because the next this he knew freaking Red Hood was behind him asking to talk. Our favorite ghost boy wouldn't be embarrassed to admit he let out a small squeek before bolting out the door yelling, "I'm not even a criminal!"
It took Jason a few seconds to process that the guy he had tried to flirt with ran away in terror. Crap.
Day three and four were blissfully Wayne and bat free, though he did find out that Tim Drake and Red Hood were looking for his two false identities. Joy.
Day five he met the stabby Robin who very valiantly beat up two people who had been following him. Danny didn't even notice he was being followed and thanked the bird for saving him. Danny, who was shape-shifted into a very pretty girl at the moment, offered to buy him something to eat as a thank you. "Danielle" insisted and Robin allowed it. Danielle never noticed the slight pink on Damians cheeks as they went over to one of Damians favorite restaurants.
Day seven he had went out as blondie and got confronted by some girl named Barbara. She was nice and managed to convince him to come to a Cafe with her. He told her his name was David and he ran away from his parents with the help of one of his friends family members and that he was Jewish, which was true...except for the David part. He learned that if you wanna keep your story straight keeping to almost truths was your best bet. She in turn told him about Tim and how he's a friend of hers-uh oh- and that he's been looking all over for him.
Danny-David- tells her he's sorry but he didn't mean to offend Tim and doesn't want any trouble before laying down enough money to cover his half of the bill and the tip and booking it out of there
This repeats with most of the family trying to flirt with him or adopt him into the family when he's out as Danny.
Bruce Wayne approached Danny when he was waiting to board an elevator, "Hel-" was all the billionaire could get out before Danny cut him off "Hell no." And then he just got in the elevator and pressed the close doors button and was gone again.