The inability to feel pain is called "Congenital Insensitivity to Pain" (CIP). It is a rare genetic condition where individuals cannot perceive physical pain from birth due to malfunctioning or absent nociceptors, which are the nerve cells responsible for detecting pain. This condition can lead to serious health risks because pain acts as a warning signal for injuries or illnesses, and without it, people may unknowingly hurt themselves or have untreated medical issues.
A particular form of this condition is called "Congenital Insensitivity to Pain with Anhidrosis" (CIPA), which also includes the inability to sweat and regulate body temperature, making it especially dangerous.
In summary, the general term for not feeling pain is congenital insensitivity to pain or congenital analgesia.