The short answer is “no,” you do not need to use your actual address in whatever country you live in.
When we register a LLC in the USA, we need to specify the “physical mailing address” for the LLC. For most states, this address can be located “anywhere in the world,” it just cannot be a PO Box. The three exceptions that I’m aware of, are Arizona (AZ), California (CA) and Oregon (OR). AZ and CA require a “physical mailing address” to be located within the state, which OR requires not just an address within the state, but has specific rules prohibiting CMRA’s (i.e. virtual mailboxes and offices, like the local UPS store).
Therefore, if you have an India physical address that will not destroy your anonymity, that would be fine. Otherwise, you want to use any address that would qualify, as long as it’s not a PO Box. We offer a virtual mailbox service that can be used. In the USA, UPS offers mailboxes that provide a street address, and those are fine too.