It may not be random, but it may have changed over time.
For example, the older HL jeans line was white on black, but now there is no longer a jeans line. Rather, it has merged with the main line. So, now just the jeans themselves still have the black on white label. In Japan, too, we have Helmut Lang socks and underwear which are made with a black on white label that just says "Helmut Lang" (no small "jeans" superscript).
Before HL did made to measure and before Prada, many of the suits and shirts had the white on black label (I have a suit from several years ago with just this label).
My more recent lighter colored shirts/tees are white on white while dark shirts are black on black.
Perhaps it is possible that runway items are usually black on black and basics are white on white, but I think that they are pretty loose on this policy if it is. So, in effect, I think it is most random or based on the color of the garment, with a few exceptions.
John