On lordshiplane.co.uk the following from a book titled East Dulwich by John D Beasley:

In A View of Dulwich, Peckham and Camberwell around 1300 Rosemary Warhurst records that in 1340 there was a hamlet called Est Dilewissh where William Mabuhs, a marshall, sold houses, gardens, arable lands, heath and enclosures to John Leverich. This was near a lane called Grenelane. East Dulwich remained a rural area until the second half of the nineteenth century.

It doesn’t say whether the name East Dulwich comes from Est Dilewissh or simply by being east of Dulwich.

http://www.lordshiplane.co.uk