Bah! There's a parameter that controls the return of neighborhood names, but Yahoo put it in the wrong parameter block! From the documentation:
FLAGS PARAMETER The input parameter named flags determines which data elements are returned in the response.
But that's NOT where the neighborhood-name parameter goes; it goes in...
GFLAGS PARAMETER The input parameter named gflags affects how geocoding is performed for the request.
A Return neighborhood names for each result.
Great service, Yahoo, but bad organization on that one.