The standard degree is "Computer Science," which is offered at most colleges. A Bachelors of Science (B.S.), a four-year degree, is usually enough, though some people go further and get as Masters or even a Ph.D.
The standard name for the job is a "Software Engineer," though there are other names for programming jobs.
There are sometimes Computer Science classes late in high school, which can help prepare you.
There are other paths of course, but this is a very good start.
Finally, you can start to learn some right now! Using a website like codeacademy.com, you can start to practice programming even now. I started writing simple games when I was around 6th grade, and gradually wrote more and more complicated ones up through college, which really helped me get my degree and then my job.