I think that the anciet empires of the Indian sub-continnent can't be called The Indian Civilization.
Today they are united under the defenition of India, but back then it was just a crazy idea.
It was like a Mesopotamian Civilization, or North African Civilization.
As far as I know, the united national defenition of Indian people became common during the British tule. (If not, then maybe in the Mughal/Maratha times, but I don't think so.)
Before that, India was mainly a geographical term.
You can clearly see the difference between several groups in the indian history.
The problem is how to name them. So this is my suggestion:
- Magadha, which mainly refers to the Mauryan Empire and the Gupta Empire....
- Kannada, which mainly refers to the Rashtrakuta Empire, the Chalukya Empire, the Vijayanagara Empire, kingdom of Mysore...
- Marathis, which mainly refers to the Maratha Empire.
- Tamil, and I see you have already put them in.
- There are much more smaller groups, but I assume you got the idea...
I think that the term Indian Civilization can only refer to the modern unified indian people.