"Grid" is as good a name as any: See Regular Grid in Wikipedia: In particular, see the "related" grid: the Cartesian Grid:
> "A Cartesian grid is a special case where the **elements are unit squares or unit cubes** [cubes in the case of a 3-D grid], and the vertices are integer points." [brackets, bold-face mine].
You could also refer to this sort of "playing field" in a game like battleship as an **incidence matrix** of sorts: where a cell in the ith row and jth column might be occupied, using "$1$", or not occupied, using "$0$".