Hello there,
No, 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 admission process. But in this case, you don't need to be tensed. Also, NTA would notify you if your admit card is not be issued due to any problem. If you haven't received any email regarding this, then you are safe. 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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