Typically, the noise in a third member is due to the ring and pinion setup. Nat always, but the vast majority of the time. If this is the case, then the noise would have been there prior to the wheel bearing replacement.
The questions I have are:
Does the third member make the noise under acceleration or on the overrun (deceleration)?
Is it noisy all of the time?
And, as Grim asks, was the noise there before or was it being nasked by the wheel bearing?
It matters. If it is noisy all of the time, another bearing (I would think the pinion set) is most likely the root cause. Noise under load or on the overrun is backlash in the pinion setup.
I recently went through the "sort out the noise" issue with the Currie third member I have. In my case, it turned out that both shafts were bent, all of the bearings were shot and... there was 0.016" of backlash in the setup. Once the shop was done with the axle, it became acceptable. Should have replaced the gear set as well though...