Spell mistake in surname on 10 the certificate as chilkamarri, whereas in birth certificate, passport and in aadhar it is chilakamarri
It would be a problem for you in the future as 10th certificate serves as your identity in many fields coming up further in your life. So I suggest you to change the name in the 10th certificate which is a long process but is mandatory.
All you have to do is write a letter to the highest authority of board and get it signed from the head of tbe instution you have studied in and send it. You will be issued a new certificate. You have to do notary affidavit for it.
But make sure that your surname is same in all the important documents like the birth certificate, passport, etc and all those you have mentioned above.
Make sure your surname is printed correct in all documents. If the one that is printed in 10th class certificate is right then you will have to change it in birth certificate, passport and aadhar card. But if the one that is printed in these documents is right get it changed in 10th certificate by following the above process I have mentioned.
Plan in such way that it wont stop you from attending NATA. If you have enough time please write a letter to higher authority of the board and prepare a notary affadivit immediately. So that it won't effect you from attending NATA.
For GRE there is no requirement of 10th cerficate. But they may ask for it when you join a job. Hence if you make necessary correction now. It will be helpful for you.