The name of the organ responsible for filtering blood and producing urine is the kidney. The kidneys are essential components of the urinary system and play a vital role in maintaining the body's fluid and electrolyte balance. They filter waste products and excess substances from the blood, excreting them as urine while reabsorbing necessary nutrients and water. This filtration process helps regulate blood pressure and pH levels. The kidneys also produce hormones that regulate red blood cell production and calcium metabolism, demonstrating their multifaceted importance for health and homeostasis within the body.