My experience is the opposite. People often use only the last name, and first name is seldom used. E.g Mr. Kumaraswamy or Ms. Deshmukh in professional context and simply the last name in friend circles.
I think it started when British started asking for surnames in job application in colonial India. South Indiana took their birthplace as surname along with caste name. In North, Singh and Kumar were used as surnames. Caste names became quite popular in late 20th century.
Before British, I am not sure if surnames were common anywhere in India. Would be a lovely study in history.