There is very least possibilities that Your mother's or father's Aadhar Card will be required at any step , so logically there should be no problem but sometimes they ask why there is discrepancy in names at yhe time of document verification if you have a reason then they take affidavit from you and you get admission.

Mostly 10th Marksheet is required as a date of birth proof these are very minor mistakes they will understand

At the end Your name should be correct and date of birth

Good luck..