Is there a proper way to name diagonals?  Is it supposed to always be left to right, bottom to top, or is there no convention?

I think you name the endpoints, e.g. the a1-h8 diagonal and so on.

EDIT: Oops, I see what you mean. Well, in the example I gave, you go from a to h and from 1 to 8, with a-h being "stronger" (i.e. the opposite diagonal would be a8-h1 and not h1-a8). This is what I've mostly seen in the literature, but I'm not certain about any official way.