Although cycling-related hand numbness can come from the neck/back, it is much more likely to come from pressure on peripheral nerves just beyond the wrist where you lean on the handlebars.
Most common is pressure on the ulnar nerve which causes numbness of the little finger and the adjacent half of the ring finger and corresponding part of the palm. Some people get 2.5 rather than 1.5 fingers numb.
Second most common is the median nerve which leads to numbness of the thumb, index, middle and adjacent half of the ring finger plus the corresponding area of the palm. Again, some people get 2.5 numb digits rather than 3.5.
These problems of pressure on the nerves leading to numbess is best avoided by the methods already described:
-Frequent change of hand position
-Good gloves (eg Assos, Tuff)
-Gel or Cork bar tape
-Proper positioning & fit on the bike
At the neck level, there are THREE different nerve roots that supply the hand so I am not quite sure what kkees' chiro is saying.
C6 - thumb & index finger plus adjacent palm.
C7 - middle finger
C8 - little & ring finger plus adjacent palm.
There is overlap in the area supplied by different nerves so you may not find the numb area exactly corresponds to the areas described.