Psychology is like law: it uses names to organize information. When your prof says “Don’t worry about the names,” she’s lying. She means it when she says it but she means something different from what you mean.
Psychology uses people as icons. So your prof means don’t worry about all of the names of the researchers that don’t matter but do know the names of the people who represent major theories. You don’t have to know all of the people who worked to develop the principles of operant conditioning. You just need to know Skinner.
It’s like case law. In law school, you don’t need to know all of the cases that don’t matter. But you do need to know major decisions. Psychology works the same way. Skinner, Freud, Piaget, and Rogers all represent different areas of research and different approaches to psychology. Skinner represents all of the rat, pigeon and animal training. Freud is the icon for psychodynamic thought. Piaget is the representative of developmental stages, and Rogers is the figurehead of counseling.
The trick is knowing which are the big names you need to remember. It will come with time. The more time you spend in psychology, the easier it will be to make distinctions. As a head start, check out the people listed in Great Minds.