You will be able to write your exams as they will only be checking your AIIMS application sheet.

You will face problem during Counselling if selected. While your documents will be verified, you need to submit your +2 results copy. The officials have the sheet of roll no corresponding details with them. Now you will get an admit card because they dont validate your information during the time of the exam. But there will be an issue during counselling and admission procedure. But this doesnt anyway effect your eligibility or merit and so this can be neglected by the authorities. They only check if that hall ticket no# bearing candidate is you and if you have scored the marks that you wrote in the application form as they will neglect that issue. So we would suggest you not to pani you better concentrate on your exams, and later this part may be handled if you get selected.