Different ways to name a baby

In India, there are various ways to name a child depending on region, religion, caste, etc.

In north India , usually a child is named typically in the following format :
first name (this can be any name),
middle name (father's name),
last name (father's last name , which is the family name)

But I have noticed, in the southern part of India the formats vary.
eg:
1.
first name (this can be any name)
middle name (no middle name)
last name (father's first name)

2.
first name (this can be any name)
middle name (no middle name)
last name (village name)

Do you know any other format ?