I've been pondering over this prospect for a while and I feel that a lot, if not most, names mentioned just feel old (most of these names sound like something my grandparents bought when they were young) and not representative of where Lincoln is trying to go (relatively youthful and 'alternative').
Anyway, I loved the name of the Ford concepts of the mid- to late-2000's so I feel those should really be brought to life, with a bit of an astronomy theme (it is the Lincoln star after all).
Focus-sized car: Iosis
2-seat sports car: Atria (a cookie for they who spot the possible irony here - http://en.wikipedia.org/wiki/Alpha_Trianguli_Australis)
MKZ: Evos
MKS/Continental: Orion [final gen. Falcon codename] - but I'm happy with Continental
LincStang: MKR (sounds good to me... Don't look at me like that!)
Full-size sedan: Centaurus (ONLY if the Taurus dies IMO - pending a rethink)
Full-size coupe: R (maybe a 'sporty' sounding constellation?)
MKC: Vertrek
* dons flamesuit* MKX: Aviator [iMO should be an inbetweener model, 5 seat only etc.]
Navigator: same
Oh yeah, there's a few 'dream machines' in there!