i think i have read that the nut of donuts is from knot or knob, as in a dough knot.. and yes, the hole in the doughnut is to make it cook more evenly..

it's is less of problem with raised (yeast based dough) donuts -- and jelly filled ones are almost always of this kind, but more of problem with "cake-like" or soda leavened dough nuts -- these tend to be heavier, and can be leaden..
the very opposite of KK's (Krispy Creme's for non-USers-- a brand of very light, raised donuts)

FF, didn't some of this come up when we discussed Tim Hortons? have you searched for Hortons? or Tim bits? i think it was in a sports thread of all places, and it wasn't me who brought it round to food!