Place chicken legs in a large saucepan over medium heat. Add onion, green bell pepper, hot chile pepper, red bell pepper, and garlic; cover pot and cook until soft, about 30 minutes.
Pour chicken stock into the saucepan and bring to a boil; simmer until chicken is no longer pink at the bone and the juices run clear, at least 45 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C). Add name root, corn, celery, carrots, recaito, sofrito, and cilantro. Cook soup until vegetables soft, at least 30 minutes more.
Stir orzo and oregano into the soup; cook until pasta is tender, about 15 minutes.