Can I stop someone from using my late father's name for a business without permission?

This is a nuanced area — personality and publicity rights in India are still evolving through case law rather than a single comprehensive statute, but courts have increasingly recognised that using a well-known person's name or persona commercially, without authorisation, particularly in a way that suggests a false endorsement or connection, can be legally challenged.

If your father had a distinctive reputation and this use is genuinely creating confusion or falsely suggesting a connection to your family or his legacy, you (as his legal heir, in appropriate circumstances) may have grounds to seek an injunction stopping the unauthorised use, particularly if it's misleading the public or commercially exploiting his reputation without consent.

The strength of such a claim depends heavily on how well-known and distinctive your father's reputation genuinely was, and how directly the business use trades on that specific reputation, rather than just coincidentally sharing a common name. Given how fact-specific and legally evolving this area is, it would be worth consulting an intellectual property or media lawyer to assess the realistic strength of a claim in your specific situation.