According to this post at Autoblog.com - Lincoln will not be calling the new Lincoln Aviator the Lincoln Aviator. (?!)
It appears that Ford has decided that the real reason Cadillac is kicking Lincoln's butt right now is the abandonment of names for alpha strings (think how Catera became CTS, Seville became STS, etc.) I'm sure it had nothing to do with billions of investment, brand new chassis and powertrains, and really targeting the standard of BMW, Mercedes, and Audi with their cars rather than chasing Lincoln.
The Aviator will actually be badged the Lincoln MKX (hmm, looks quite a bit like Mark X, don't it?).
We'll see how this goes for them - but ultimately, I think great product is the only answer - not new names.