The names proposed seem all intuitive and improving over the old
nomenclature. Nevertheless, I'd point that the expression:
|(x − Xi )| + |(y − Yi )| ≤ dist
actually defines a circle, not a diamond (this is obvious when dist
is, say, larger than 5). And indeed it is a circle that we are
expecting here. So in this particular case the method name could need
some more work.
On a further release of the manual some illustration of these
different types of neighbourhoods, with different dist values could be
helpful.