Answer:
A Patronymic name is a name based on the personal name of one's father. Patronymics were widely used everywhere in past centuries but most present-day western countries no longer use them, nore does China. Use of patronymics is common in South Asia, the Middle-east, and Iceland, among other places. Patronymics are also used in the Russian language along with surnames.
Using English names as an example, if John has a son named Thomas, Thomas would be known as Thomas, son of John, or as Thomas Johnson. If, then, Thomas has a son named James, James would be James Thomasson. Eventually, patronymics became transformed into surnames, in some parts of the world. That is why there are now family names such as Erickson, Johnson, etc.
Similarly, in southern India (Tamil Nadu & Kerala) where patronymic names are common, consider a person whose personal name is Vineeth and his father's personal name is Sreenivasan. Vineeth's full name would be Vineeth Sreenivasan. This shows that he is the son of Sreenivasan. And if Vineeth's son's given name is Rahul; Rahul's full name would be Rahul Vineeth.