I found some marketing mock ups that included the name "VeriPhonezon".
Obviously fake. Way too short. The device will almost certainly be called something like the Droid Omnipotent vPhone With iCast (TM).
(I really hate Verizon's marketing.)
Of course, there's plenty of caveats in the article about legal wrangling to end it earlier. So, all this tells us really is that the original contract was a five year exclusive.
I imagine Apple has had the option to drop this agreement due to breach of contract or failure to perform or some clause like that. During last year's iPhone event Apple made it perfectly clear they were not happy with AT&T's performance. AT&T has bobbled or dropped the ball on many occasions (including MMS and tethering). I assume the exclusivity agreement could be declared null and void due to AT&T's incompetence.