I think it's just an animal control officer for most state's, it's when you get into the bigger cities, such as in CA, or detroit MI, that they become animal cops due to the over population of animals in these areas, the neglect is usually higher. Also there are more people who use dogs for fighting purposes, and such.
the title of the job is animal control officer. it is not really a major in college. its more like a 6 month training course. at least it was 20 years ago when i took it and became certified. it was offered through one of the colleges in my state. after you pass the certification class you are required to continue with some continuing education. i am not sure if there is a national organization to belong to , but there is a state org. in my state that you have to join.