This is a pretty common question. The following is from a post that David Conant (one of the earliest employees of Charles River Software/Revit Technology Corporation) made at the AUGI Revit Community forums in response to the question. There is also a list of the names they considered in that thread.
The Revit name is an invented word designed to imply revision and speed. Since our original name idea Perspective was taken by a spec application, we (Charles River Software at the time) hired a public communication consultant to assist in developing a name. Revit won out over a number of other proposals inlcuding Archadia and the one I found the oddest, Estuary. In the end, although it seemed unique, Revit was also being used (and still is I believe) by a Dutch manufacturer of leather motorcycle clothing. Despite the number of interesting mispronunciations and parodies I have heard, the name seems to have worked quite well.
Here is a list of the possible names that Irwin Jungreis (one of two founders of Revit) shared.
Anyware, Associa, Cambient, Cyclorama, Datrix, Delta Point, Ditto, Dymension, Kaleido, Resonant, Reverberant, Sequent, Synchronix, Synsym, Vium, Occulus, Revkor, Staccatto, Whole Building, Elevation, Parabuilding, VantagePoint, BuildBase, Parapet, Edifice and DesignIT
Irwin also wrote, "Everyone in-house liked the name Edifice, but when we mentioned it at a focus group with architects their faces turned sour and that name candidate was eliminated in a fraction of a second. (Side note: while we were researching that name, we found a demolition company called Edifice Wrecks!)"
To read the thread yourself CLICK HERE. You'll probably need to log into AUGI.