Given how often they've been arrested, tried, and either convicted, had cases dismissed due to evidence being fruit of the poisonous tree, or been found incompetent to stand trial and sent to Arkham, I suspect that the real names (when known) of Batman's rogues are all matters of public record. While the public may still know them by their nicknames/codenames/etc., the real names would be fairly commonly known, much like how most people know David Berkowitz better as the "Son of Sam," but would still recognize his real name.
I know that, in the DCAU, at least, Selina's real name is public knowledge, following her trial and conviction in season one of BTAS.