Well the rule says that your name in the adhar card should be same in all of your documents ,whether it is your application form or it is your certificate. In jee yes they see your photo but your name should be same , because when you go to the reporting centre they first see your name. 

You can expect that it doesn't cause any problem , but if it cause you can make affidavit stating that both the person are same.

All the best.

Thank you.