Peter was raised away from all other Lightwoods, his father not getting along with any of his family. After he had died, it was his mother who took on giving reason not to have contact with them. And then she also passed, which left Peter with nothing but names and a location. New York Institute, Alec, Isabelle, Max, Maryse and Robert. Not much to go from, but it was enough for the boy to find himself in New York days later, locating the institute and presenting himself as Peter Lightwood.
Seeing as Izzy was out on a hunt with Jace and Clary, they sent for Alec, hoping to take care of the intruder/visitor. As far as they knew, there was no Peter Lightwood. He hadn’t been written down into any family tree, never registered, and they had no reason to believe him. Peter now stood near the entrance of the institute, wearing jeans and a jacket which covered too much of him for them to see whether he had any runes or not. Somewhat cornered, he was having a small argument with one of the Shadowhunters who claimed that there was no such thing as an unregistered nephilim; that Peter had to be lying.