Hi sir/madam, you have to give one representation to the concerned hospital and local birth and death registrar office for rectification of the surname in the birth certificate and in the hospital records. If the hospital and registrar refused the same, you have to issued a legal notice u/s 80 of the Code of Civil Procedure, 1908 for statutory period notice, after completion of the statutory period notice, you have to file civil suit for declaration of change of surname from old to new in the birth certificate and hospital records etc.,. After decree of the suit, you will produced the said decree before the registrar of death and birth, hospital and etc.,. they will rectified the same. It is the procedure.