Sending the head would seem to be the work of a truly sick individual, no question about that.
I do have questions that nobody here can answer.
1-How did the dog die?
2-Did someone kill the dog just to ship the head?
3-Did it get hit by a car or some other accident, then somebody found it, knew who owned it and decided to be a dick?
4-Killed the dog for some other reason, like aggression, excess barking, crapping on their lawn, then decided to be a dick.
I could go on but #1 is primary.