My family is from South India. The traditional naming convention in our community for males is:
[Caste Designation or Community Name] [Family Name] [Given Name]
The result of this is that people using this naming convention (who belong to the same community or caste) will have the same first name and different last names.
However, for reasons which I have not been able to determine, some families in the community traditionally used the following convention:
[Family Name] [Given Name] [Caste Designation or Community Name]
Large numbers of our community have immigrated to the US. For their first generation children, some of them have chose the following naming convention:
[Given Name] [Caste Designation or Community Name] [Family Name] [Father’s Given Name]
This approximates the US convention of having the given name first, and keeps the child’s last name the same as the father’s last name (because the father’s given name is his last name).
Other members of our community have chosen the following naming conventions for the first generation children:
[Given Name] [Caste Designation or Community Name] [Family Name]
[Given Name] [Family Name] [Caste Designation or Community Name]
This follows the US naming convention, but has the effect of the first generation child having a different last name than the father. Subsequent generations wouldn’t have this problem, however. (I’m named according to the latter convention)
For women, this is a bit trickier. From what I can tell, many women traditionally only had their given name. However, these were the traditional naming conventions used for women in our community:
[Given Name] [Father’s Given Name]
or (but I’ve rarely seen this):
[Given Name] [Family Name]
After marriage, the wife would use the following convention:
[Given Name] [Husband’s Given Name]
[Given Name] [Husband’s Family Name] [Husband’s Given Name]
and I’ve seen this one for women:
[Given Name] [Wife’s Family Name] [Husband’s Given Name]
and this one too:
[Given Name] [Wife’s Family Name] [Husband’s Family Name] [Husband’s Given Name]
But all the older married women I’ve seen always have their Husband’s Given Name as their last name.
And I’ve never seen a woman in our community use the traditional naming conventions for males (which I described above). However, the first generation naming conventions which I listed above for the children of immigrants is being used for females as well as males.
And if that’s not complicated enough:
Members of our community who are still in India are beginning to adopt the naming convention which the US immigrants have adopted.
These naming conventions are for our community. Different communities will have different conventions, however I think something close to this is fairly widespread in South India.
As for the initials, it’s common to initialize the first two names when using the traditional naming convention for males. It’s also common to initialize lengthy names as stated above.