Spray the inside of a 6-quart slow cooker with nonstick cooking spray.
Place the chicken breasts in the bottom of the crockpot.
Add the diced onion, minced garlic, black beans, corn, diced tomatoes, enchilada sauce, chicken broth, and green chiles.
Sprinkle in the cumin, chili powder, smoked paprika, dried oregano, salt, and black pepper.
Stir the ingredients gently to distribute the seasonings. Make sure the chicken is mostly covered with the liquid.
Cover and cook on LOW for 6–7 hours or HIGH for 3–4 hours, until the chicken is tender and fully cooked.
Remove the chicken from the slow cooker and place it on a plate. Shred it with two forks.
Return the shredded chicken to the crockpot and stir it into the soup.
Add the softened cream cheese. Stir until it melts into the hot broth and creates a creamy texture.
Stir in the shredded cheddar or Monterey Jack cheese until melted and smooth.
Add the fresh lime juice and taste the soup. Adjust the salt, pepper, chili powder, or enchilada sauce as needed.
Ladle the soup into bowls and serve with your favorite toppings, such as sour cream, cilantro, avocado, tortilla strips, cheese, and lime.