The upstairs area was called the Ledgerdemain Lounge (note the extra "d" in the name) leading to confusion over the name. It was likely just a typo when creating the subzones, or at the time they were created the need for separate subzones for the hearthing mechanics may have been required. The upstairs subzone was eventually merged into the first floor during the Mists of Pandaria expansion.
In the November Issue of Kirin Tor Monthly, it describes an inn called the Hocus Pocus Inn alongside A Hero's Welcome and the Filthy Animal. As this inn does not exist in Dalaran, it may be an earlier name for the Lounge.
Legerdemain is actually an English word that comes from the French "légèreté des mains", meaning "lightness of hand", which is more commonly called "sleight of hand" in English. This refers to Dalaran being a city of magicians, since sleight of hand is an essential skill for real-world magicians who wish to perform convincing illusions.
Patch 5.0.4 (2012-08-28): The upper and lower floor subzones have been combined into a single one.