I have booked a ticket on IRCTC (Indian Railway Catering and Tourism Corporation) for me and my brother but now even my sister is willing to travel but we are not getting tickets for her. So my brother agreed to not come and take my sister with me. Can I take my sister on the same ticket which is booked on my brother's name? Or is there a way I can change the name on already booked ticket to reflect my brother's name or is there a way I can cancel the ticket and book the same ticket on my sister's name?
Yes, you can do this. Here are the details on the official site: Change in the Name of Passenger
Change of name of a passenger having a seat or berth reserved in his name in the following circumstances namely:
(b) Where the passenger makes a request in writing 24 hours before the scheduled departure of the train that the reservation made in his name may be transferred to another member of his family, meaning, Father, Mother, Brother, Sister, Son, Daughter, Husband and Wife.
As the rules state, you need to do this at least 24 hours before the journey.
Based on my experience, you should take a printout of the page linked above--there are some booking clerks who don't know the more obscure rules.
The intention of this answer is to serve the generic question of is name change allowed more than to answer the original poster because we don't want duplicate questions to be improperly answered.
As someone who has been a booking clerk myself I can clearly state this, change of booking is not handled at the lowest level. Since travel agents can misuse this provision to book tickets in fake names and then later transfer it to someone else, regardless of the rules, it cannot be done is a safe assumption to make.
While the above stated rule is correct, you will practically find that in most cases you will be denied this "facility" because "Chief Reservation Supervisor of important stations are authorized by Railway to permit the " is missed from the previous answer which is extremely important, you wont be able to do it in most stations without great difficulty, this is the practical answer.
Also another important point is "Such request will be granted only once."