Is there a name for the problem of spatially organizing a graph as to minimize total edge length?
This is a version of graph drawing, restricted to vertices being on a grid, but allowing more than two dimensions.  The one-dimensional case is an example of a graph layout problem, known as Minimum Linear Arrangement. In all of these problems, one is interested in minimizing some metric of the resulting diagram, which could be the number of edge crossings or, in your case, the total length of the edges.

These kinds of problem are very often NP-hard, even in the one-dimensional case: in particular Minimum Linear Arrangement, the 1D version of your problem, is NP-hard. There's a survey of graph layout problems by D&iacute;az, Petit and Serna (ACM Surveys, 34:313&ndash;356, 2002; .ps.gz).