What is hereditary rule by one person known as?
The most likely answer to your question is “monarchy.” Monarchy is the term that applies to almost every system of government in which a country is ruled by one person who gains their political legitimacy from their membership in a given family.
In a true monarchy, the ultimate authority rests with one person. We typically call that person the king, the queen, or the emperor. While that person has certain pressures on them to rule in particular ways, there is no one who actually has the legal authority to overrule them or to tell them what to do.
In a monarchy, power is hereditary. Queen Elizabeth I of England had the right to rule because her father had been King Henry VIII. She was selected because of her bloodlines, not because of her political skills or her charisma. The same held true for all monarchies, which is why monarchies would occasionally fall into civil war when a monarch died and there was no single person who was clearly the most closely related to that monarch. Since power was supposed to be hereditary, tremendous problems could arise when there was no person who clearly “deserved” to inherit that power.
Not every country that has hereditary rule by one person is called a monarchy. We do not call North Korea a monarchy even though it has now had three autocratic rulers, all from the same family. Kim Il Sung took power when North Korea became a country. His son, Kim Jong Il replaced him when he died. When Kim Jong Il died, his son, Kim Jong Un, replaced him. This country certainly appears to be a monarchy, but we do not call it that because it claims to be communist.
Countries like North Korea notwithstanding, the best answer for this question is that this type of governmental system is called a monarchy.