No, this will not become any problem during MBBS studies, also you can update it through aadhar enrollment center. Mostly exams application forms asks for aadhar number you should write correct name of yours in application form.

Dear Joshua, get an affidavit done stating that both the names the one im Aadhar Card and the one in other documents belong to you. But the Supreme Court has passed an Order last year Stating that Aadhar Card is not a mandatory document for educational purposes. So even if you do not submit Aadhar Card it is ok. But if you want to submit it, just get an affidavit done please.

It's better to get it corrected, as adhar card can be updated online as well as in any nearby centre.