Determine whether the mistake was made by you during the completion of the online application form, or by an embassy or consulate officer during the processing of the application.
Contact the consular or their assistant directly at the embassy that issued the passport and explain the problem. Ask them to reissue the passport with the correct name as soon as possible.
Email the passport office of the Indian government if you are unable to speak to anyone in authority at the embassy or consulate. Clearly outline the problem and ask for an urgent solution.
Mail or visit the nearest Indian embassy along with the passport requiring the name change. Depending on who was to blame for the error, you may have to pay a fee of $40 -- as of April 2011 -- or this charge may be waived.
Check the new or reissued passport carefully for further errors or signs of damage.