It is under Verizon's discretion, but if they don't call it the Droid ___ then it's not a Droid. It's just an Android OS powered phone. Technicality more than anything else really. For instance, they didn't label the Thunderbolt the Droid Thunderbolt so calling it that would technically be incorrect.
All I'm saying is that if BING is the only thing separating Droid from all the others then that's not enough for me to thing I have something special. I mean I hate BING anyway. I just think, even still, that Droid is a brand name only and that Droid phones are pretty much the same as other android phones. Maybe Microsoft has a deal with Motorola and that's why those phones have BING, which I think is more likely than it having BING because it's a Droid.