Hello,

Yes, you can still appear for JEE Main entrance examination. You should actually fill your name, father's name, mother's name and date of birth as per class 10th certificate. So as you have given your name as per class 10th certificate you won't face any problem. Adhaar card is for photo identity purpose. So if you will be carrying Adhaar Card to the examination center you won't face any issue, if is for identification purpose.