This is the simplest, plainest and probably the most obvious hexagonal neighbourhood imaginable.
Previously this neighbourhood has been known as the "Uniform" neighbourhood (e.g. see [ the pages of Charles Herring]).
It has also been called the "Hexagonal neighbourhood" e.g. [here].
This name seems too broad to me - as there are a large number of other hexagonal neighbourhoods.
"Honeycomb" appears to be a superior name to (say) "graphite", as far as images of planes tesselated with hexagonal tiles go.