Lewis did a pretty effective job of getting his name and face out there. Not everyone follows on-line forums but he was a consistent presence in marketing materials, Disney Files and other
DVC tie-ins.
And I do firmly believe that the more voracious fans (like ourselves) would be worked into a proverbial tizzy if several months went by with no word of a replacement. There's a member cruise a month from now and the annual meeting in less than 4 months. Those are perfect opportunities to immediately earn points with some of the most critical elements of the membership base.
Beyond that, it's not just about members. DVC has ongoing relationships with vendors, contractors, local government officials, business partners such as RCI, lending institutions, and so forth. Someone needs to pick up those relationships immediately. This isn't a forced retirement situation where his duties can be transitioned to a successor over the next few months--Lewis was shown the door. There are decisions to be made, projects to manage, egos to smooth, hands to be shaken and so forth.
Internally people need to know who is in charge at DVC. The new head has work to do and doesn't need to meet resistance from staffers who are unaware that he/she is Lewis' super-secret replacement.
DVC is a multi-million dollar division of a multi-billion dollar, publicly-traded corporation. The incoming head doesn't have the luxury of staying in the background, glad-handing sales booth agents for a couple of months while others make critical decisions and repair any damage left by Lewis' abrupt departure.
In the end, I don't see any value to the new head remaining anonymous. He/she can still spend spare time getting to know front line staff members. But there is unquestionably work to be done. A fair amount of member anxiety--even if largely limited to the DIS and similar forums--can be placated with an announcement and a few select public appearances.