The usual norm is that the details on the 10th marks sheet are considered for admission and counselling purposes because that also serves as the proof of your date of birth. Now because the rest of the documents have full name, you should get an affidavit done stating that both these names belong to your father. That way even when you appear for counselling and admission, you will not face any issues.

You just contact a lawyer near you and he will guide you out regarding the affidavit.

I hope my answer helps. All the very best for your future endeavors!