Peckham Rye / East Dulwich, they're just words. If someone is going to commit a crime they're not going to think - "Here's an invisible line I must not cross because no-one cares about a place with the word Peckham in it". Enjoy the area. The park is fabulous and in a way you're in the middle of a lot of useful areas. Two stations, loads of bus routes, a fabulous park, great shopping streets, Rye Lane and Lordship Lane depending on what you want AND another fabulous little shopping street Evelina Road in Nunhead (Sopers and Ayres for example), the best doctors anywhere, being Nunhead Grove which is near you. But don't just live there, join the community and be part of it. The Peckham Society, The local community council, the police ward panel for your area, and others things. Be happy and hope you enjoy it there/here!