I am not aware of any school that offers a degree in talent management. However, there are a couple of ways you can go about deciding your major and choosing the classes that will help you pursue a career in the field.
You should ask yourself some questions:
What kind of art form are you wishing to manage: visual arts (photography, painting), music (classical, pop, jazz, country), dance (ballet, jazz, pop), theater (drama, broadway), etc.
Do you already have some skills in your art form of choice? Do you play an instrument, or dance, or sing?
If you already have an art form you love, and to which you have dedicated some time learning, I would use that as your starting point. Maybe look at getting either a subject-focused degree (music performance, dance performance, visual arts, etc) and compliment the class curriculum with business and general administration courses. For example: pursue a bachelor of arts degree in piano performance, with a minor or double major in business administration and/or entrepreneurship. You can also pursue a degree in liberal arts, and divide the course load between arts classes and business classes. If you are more business-minded, pursue a degree in business administration, and add many classes about the art form you wish to manage.
What does an artist need from his/her manager? In my humble opinion, they need someone who understands their art form enough that can comfortably establish a dialogue with the artist and the presenters. They also need a person who has enough knowledge and connections in the chosen field to help the artist navigate the market. The artists need a person who is passionate about the art form and about working with him/her. They need a person they can trust so they can forget about the business side and focus on their art.
I have worked in the talent management field for a number of years, and my path to this career was more serendipitous than purposed. I focused my early studies in music performance (viola being my main instrument), and took many courses in music history, theory, composition, and anything else that gave me a deeper understanding of classical music, my art form of choice. When I started looking for jobs, I decided I would not pursue a career in music performance, and discovered that together with my other skills (organization, good communication, curiosity for the field, creativity, and people skills) I could pursue a career in management. I love people and working with the creative types. Working with artists then made sense to me. I knew what it meant to go on stage and perform, and what was needed to make that possible. Therefore, I could have a dialogue with other artists and help them pursue their careers and dreams. As many other fields, you have to start from the bottom up, and work with more seasonal managers as you learn more about the field.
Whichever undergraduate degree you think makes sense for you, make sure you compliment that experience with internships in the field. Many management company offer 4-month internships during the school year and in the summer. You should also consider internship in presenting organizations like orchestras, theaters, concert venues, etc.
Please keep writing if you have any more questions. I do hope you find this helpful.
There is not a clear path to become an artist manager, which is the best news. You can create your own path to your desired job.