The Pope's nose, parson's nose, or sultan's nose is the common name for the pygostyle, the sticky-up bit at the rear end of a bird upon which the tail feathers are mounted. This will include the final few fused vertebrae -- analogous to the coccyx in humans -- but more importantly, it will include some fatty tissue covered in skin. This is a delicious, if somewhat hard to eat, part of the bird. It is often removed because it is very greasy and contains the bitter uropygial gland; however, with the gland removed the greasiness can make it a delicacy, akin to the bird's neck.
As a general rule, anatomists will refer to this structure as the pygostyle, while people who are more interested in eating the bird will refer to it as a powerful person's nose.