Hi. I'm Dr. Gotthelf. I have been a skin and ear vet for 35 years and I would like to use my experience to help you with your pet's medical problem.
Depigmentation of the nose can be from somethnig simple like rooting under things with the nose to autoimmune diseases. Your vet will be in the best position to determine the cause. If it is a traumatic issue, then you will have to change the dog's behaviors in some way to keep him from rubbing his nose on the ground or a door. If it is an autoimmune disease, like pemphigus or discoid lupus, then steroids may be needed. A biopsy of the area between the black and pink areas will let a pathologist characterize the cause of the depigmentation.
I don't see any trauma to his nose. Its the whole nose changing color.