"Chicago really is a big, wonderful amalgamation of unique enclaves. Where do the names for all these neighborhoods come from?"
Certainly some neighborhoods have been left out, but this list hits many of the high spots. If you grew up in Chicago or spent any time in that city as an adult you will recognize these neighborhood names and probably know exactly where they are located.
I spent the first half of my childhood in the Roseland neighborhood which borders the Pullman neighborhood, both of which are near the Beverly neighborhood. Also near Evergreen Park and Morgan Park. We thought of ourselves as being most specifically from Roseland more than Chicago.