Simply adding a middle name or inoffensive epithet to be allowed to immigrate is an interesting idea, and not one that's actually come up before—the only times I've ever seen name change requests with the intent of getting around an identical name before, they were complete name changes (like from "Alexander" to "Siegfried").
Since this rule is one that comes direct from Tom, I'll send him this topic and see if I can get him to weigh in.