Until the early 1900s or so there was never a unified polity ruling over the entirety of the Indian subcontinent, and modern India was assembled from a set of disjointed kingdoms and 'princely states', each with their own languages and cultures.

The people in the southern five states of India speak an entirely unrelated language family—Dravidian, rather than Indo-European.

In many senses India is more like the EU than first meets the eye, which is why it is so hard to govern.

I'm from South India, and in general, people's names fall into sets of common given names and common family names, but it can get tricky. Things vary state-to-state, and even within states, across castes and subcultures. However, this also makes it somewhat easier to gauge where someone is from. Over time, you recognize some name patterns and you can guess that they're from a specific place, speak a specific language, etc.

For a very generic example, if I encounter someone with the surname "Singh", I'm reasonably sure they're from the northern states, and likely speak Hindi apart from their native tongue. Also in terms of identifying someone's given name, they're usually from a broadly known pool. As an analogue to western names, if someone says their name is James or Marie, you're mostly guessing that's their given name, even though it's possible to have those as last names as well (eg. LeBron).

Regarding "Singh", generic Sikh surnames aren't discussed in the article but they are particularly useless and challenging.