Moderators have the ability to search for users by, among other criteria, display name. In my experience, this is a feature that isn't often needed, but when it's needed, it's bordering on indispensible.
However, I believe there is no way to search for users based on their past display names.
Past display names remain available (at least for a time) for moderators through the profile view, but this requires manually looking at each potentially-interesting profile in turn, at which point you pretty much know which profiles you're interested in anyway.
Can we please have a search feature that searches for users by their historical display names, as opposed to merely their current display name?