I have a whining noise coming from the rear end of my jeep.

differential noise come as whines on drive and grumble on over run
generally indicates pinion bearing failure and needs urgent repair
it occurs when the bearings fail , reducing the preload and the teeth mesh moves from the proper pitch circle mesh

rear end (I use and electronic stethoscope to find all that)
but rear end. is a big place..
bad U-joints top that list (repeat)
bad axle bearings.
brakes bad, there. or the warning devices there for early brake warn.
bad 3rd member, gear sets or bearings in same or pinion.

my guess is car is moving right>
if not moving ,its dying rat up in there.or loose parts.

if your mecanic replace the ring and pinion and the whining noise is theare again you have a big problem your mecanic dont know how to adjust the rear end the adjusment betwen the ring and pinion its critical to the llife of the rear end have a good look

Bad wheel bearing most likely.

sounds like the rear end is going out

that sounds right

Here are the common causes or rear end noises
Constant high pitched whine at all speeds: Pinion Bearings or Ring gear carrier bearings
Whine at steady speeds or whines on deceleration: Rear end gear set is worn and will need to be replaced.
Rumbling type of noises are caused by wheel bearings or a tire with a separated cord.

It could be the 3rd member bearings (rear end). Could also be syncros
in trans. Need to put on a lift and run to hear problem.

whining from the rear end is usually associated with the differential i would have the oil checked first,as low oil is associated with diff whine