The reason behind checking your Admit card and Id proof is to validate your authenticity or identification. They are usually checking if both the Candidate who has applied for the exam and who is appearing for the exam are one and the same. Even if your Aadhar card has your Mother's name and your admit card has father's name on it it is fine. That is not a reason to be worried. As long as the surnames match and it is you who is appearing for the exam, everything will be fine. But to keep yourself stress free, take any other id proof also along with you like your Voter Id, Ration Card, Passport, etc. They do not check the spellings. They check the names of the parent but identity of the Candidate. That needs to be you.