tgchar : Interesting. I hear SSA doesn't send no match letters anymore, actually, so that's good news. I was under the impression that SSA checks would reveal previous names, but that might be because it did for me (but I had to do the whole fingerprinting, full background check deal, so I appreciate the correction that this is not true for many people).
I did actually mean "credit check," like when you run your credit reports - mine does show a previous name under that SSA, and my wife's shows three (because married, maiden, and no middle name are all listed separately), as we discovered when we did buy a car last year. It is true that that data is often munged, but it's hard to rely on that to *guarantee* that an employer won't figure out the truth. You're 100% right about the only ways to avoid that particular issue...
I really like your idea of "none that would be relevant" or whatever, as that neatly evades the question of outright denying it (which can be grounds for dismissal just for "falsification of an application") without providing the previous name for them to poke at.