As per the new directive, all candidates are required to fill name as per their class 10 and Aadhar both in JEE mains form for any session.During counselling you might face some issue. And that's too because of different name on AADHAR.you should rectify your aadhar card name in order to avoid admission cancellation in future.

Moreover,10th Marksheet is usually needed to verify the D.O.B. So there will be no such issue with respect to 10th certificate.

Aadhar card is useful for present and permanent address proofs and thus correct name somehow become necessary over there.

To clear any doubt regarding JEE mains exam registration and form you can refer to the link

https://engineering.careers360.com/articles/jee-main-application-form

Best wishes for your future..