NTA has opened the correction window thrice to make changes to your NEET application form. But if you have missed that deadline, unfortunately there is nothing much that can be done at this point in time. And now the Admit cards are due for release on August 29th and so no corrections will be entertained at this point in time. But this will not affect the merit list. It means swapping your parents names in the NEET application form will not affect the merit list in any way and so you might still get the admit card. But when the Counselling process begins, you will have to make sure you enter the details correct there. Or once the admit card is released, you can actually mail NTA about the swap and they will make a note of it and allow you to the exam hall and later give you leverage during filling the registration form for Counselling. But this will not be the reason why your application will be rejected.