Rend is really weird: despite being a kind of “bonus damage,” it is worded as though it was a separate attack, albeit one that doesn’t involve an attack roll. It even says “This attack” to refer to itself in the description.
If rend is a separate attack, and the rend damage is applied to a character denied their Dexterity bonus to AC, then sudden strike or sneak attack damage should apply: both say that “the attack” deals the extra damage in this circumstance (sneak attack says the attack also gets this bonus when flanking). There’s nothing about needing an attack roll for this.
And if you are adding your extra damage from sudden strike or sneak attack, you should be increasing that damage by your level if you have Craven.
Is this reasonable? By definition, when you trigger rend, you have already struck (and applied your extra damage) multiple times already. Narratively, rend seems much more like bonus damage than it does a separate attack, particularly given the absence of an attack roll.
On the other hand, this is a character who has potentially nerfed their druid spellcasting and wild shape forms getting sudden strike, and who has equally nerfed their sudden strike damage getting wild shape. Sudden strike, in particular, is a really poor form of bonus damage, being difficult to trigger. This does not seem like a particularly high-optimization approach, which might encourage me to throw the character a bone and let rend apply sudden strike (and Craven) again. But you know your table better than we ever can, and my recommendation is (as always) that you do whatever is best for your game. If another application of sudden strike and Craven is going to chew through monsters too quickly/make this character too dominant/let them have too much spotlight, then don’t allow it.
Is the answer any different if he had sneak attack instead of sudden strike?
Well, the obvious difference is that the damage would trigger while flanking, instead of only when the target is denied Dexterity to AC.
Beyond that, strictly speaking, sudden strike doesn’t qualify for or trigger the use of Craven, because Complete Adventurer and Complete Scoundrel say
For the purpose of qualifying for feats, prestige classes, and similar options that require a minimum number of extra damage dice, treat the ninja’s sudden strike ability as the equivalent of sneak attack.
(Complete Adventurer pg. 8, Complete Scoundrel pg. 25)
Craven doesn’t require a certain number of extra damage dice, it just requires “sneak attack class feature.” Since that’s not a minimum number of extra damage dice, this rule doesn’t apply. This is stupid and an oversight, and should be ignored by any reasonable DM, but you asked.