It's something we use ALL the time. Fltplan.com holds a callsign at the FAA level, similiar to the way Mesa Airlines ("Air Shuttle") does, and extends the opportunity to their customers. Fortunately, we have the ability to use the callsign, or the actual tail number. There are times when we are going somewhere and the owner doesn't want anyone to know he's going there. Usually, the DCM callsign is for our owner flights, only, and the normal N number registration callsign when we have anyone else on board. It isn't cheap, though, but then again, considering the ease of service, it is actually very affordable. Cheaper than a ramp fee at some airports. $250.00/year/aircraft. IE N12345-$250, N12346-$250, etc, etc, etc... They can block your tail number in about three hours, too, which is great, and they assign you a callsign. IE N12345 COULD be DCM348 (something random), or "Dotcom 348" when you're calling into ATC.
It's a great service, in my opinion. The level of privacy suits our owner's needs well.
Go to
www.fltplan.com if you want to do it. Right now, there are obvious links to it on the website.