There is no “diagnosis” that fully encompasses the behavior and emotions that you have described. Answering the “why” question is not always possible, especially when I know virtually nothing about you and your personal life.
It is unusual to kill and torture animals. It’s worrisome. That puppy did not deserve the treatment that it endured. Animals are helpless creatures that rely on the kindness of humans.
The FBI has recently reclassified animal abuse as a felony (used to be a misdemeanor), in part because of the recognition that people who hurt animals are at risk of hurting people. Some communities have begun to create registries, much like sex offender registries, of convicted animal abusers. Harming animals is a serious matter.
To avoid jail time, and the prospective of being publicly shamed, it is important to do what is necessary to never harm or kill another animal. I would recommend counseling. It would allow you to explore what motivated your behavior and most importantly, to ensure that you never hurt another animal or a person. The fact that you “constantly fantasize about killing and torturing animals and sometimes animals [I think you meant to write people]” underscores the need for mental health treatment. Please take care.
Dr. Kristina Randle