I think "March" comes from "marche" which I suspect means "border" in French or perhaps Norman French (there's a part of France that is called "La Marche" and is an ancient border between two now defunct kingdoms). So maybe it is just the Norman version of "borderers" and "Border Lairds." In Norman times, those borders were about like the old Iron Curtain; heavily fortified by the Anglo-Normans against the Wild Welsh and heavily contested with them.

Someone with better knowledge and a better memory may well come along, but until that happens, "That's my story and I'm stickin' to it!"