Spoilers my a**! I've been waiting for this for nearly 4 months ever since the trailer premiered!! And I'm still going to have to wait longer for more angles!
Okay, so after reading through four pages of posts, I know I have to comment!
And here are my first thoughts: she is a monstrosity, in more than one sense of the word. Now, that is not to say that I'm trying to have a open mind. After all, I've only seen one angle.
And I think it remains to be seen what influence the Vengeance will ultimately have. After all, I doubt I would have as high a regard for Church's design if not for the designs that were influenced such as Sameulson's Perception class.
But where as the Churchprise at least has some elegance to her (albeit in a distorted, twisted kind of way), the Vengeance is most angles with the saucer section being the biggest exception being the saucer section. And then there are all these various details. Now, I love details, when they are put before the overall shape or look: not so much.
Okay, so the Steamrunner and Norway classes uses angles well enough, but the Vengeance uses a few too many angles for her own good. Maybe not to the degree of the Zephyr class, but yeah...
However, I will say this much: the lack of aesthetics was probably done on purpose. If the Vengeance was designed and built in secret, then those who contracted for her probably had only concerns for her getting completed, and being able to do the job she was constructed for. The designer they commissioned probably wasn't supposed to have been know for making stylish designs, but merely known for getting the job done, and keeping client confidentiality...
A ship this size must be comparable in size to an Imperial Star Destroyer, which isn't much more stylish (though the basic shape of the latter is somewhat pleasantly simpler. They were probably thinking "to hell with refinement and aesthetics, lets just get the d@*m thing built, and operational"!
As for the name: I think that might have something to do with the loss of Vulcan, and having a hole nearly drilled to the Earth's center. The Vengeance was probably constructed with the purpose in mind of defending against any monstrous vessels like the Narada, should any more of them rear it's ugly head. Maybe the Vengeance was also partly built in the memory of Vulcan's destruction.