@JainilK,
My domain is in healthcare tech and services, I think am somewhat capable to answer.
@UrsRafeek rightly pointed the reasons. However one major reason is one person Dr Pratap ready, founder of apollo. He made chennai popular for tertiary medical services. 3-4 decades back patient from whole india was travelling to chennai for challanging surgery like cardiac, neuro etc.
Besides that for Bangladesh & NE patient chennai and Vellore is very famous, they become that due to mouth marketing mainly.
Sometime non clinical factors plays important role, like “Afghan house” in Delhi provides convenient and low cost accommodation for Afghani patient, hence they perfer Delhi vs anyother city for treatment.
Disc: No connection with any city or hospital mentioned in my content.