My guess would be "Indian", but that sounds like a guy with a feather on his head who hunts buffalo.
Is there a better name?
The correct term (demonym) is Indian. In the United States, the term Asian Indian is also used in order to avoid confusion between Indians from the subcontinent and Native Americans (American Indians). These days, using Indian to describe a Native American may be considered improper and even offensive by some*. Thus, even in the US, Indian would often to be taken to mean someone from India. And if one wanted to completely avoid ambiguity, then from India would suffice.
*Some Native Americans do not mind being called Indians. (Thanks to @Robusto for pointing that out.)Tweet