Hello there,
NTA generally rejects the admit card of any candidate for the following reasons:
1. The application form is incomplete
2. More than one application form is submitted by a particular candidate
3. If the information provided doesn't match with the documents.

In your case, you will not face any problem, there's no need to worry. Your father's name doesn't affect the merit list. If the issue was with your name, then it would create a problem with your admit card and the admission process. But in this case, you don't need to be tensed.

Also, NTA would notify you if your admit card is not issued due to any problem. If you haven't received any email regarding this, then you are safe. Since you have sent an email to the authorities regarding this, just wait for their reply. You don't need to worry. Generally this doesn't create a problem. You will receive your admit card, and can appear for the exam. And for the counseling and admission process, you can have an affidavit, if required, stating that both the names belong to the same person.

Hope this answer helps you.
Good luck!!

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