I filled wrong name of qualifying board in jee form and couldnt get it corrected. What problems would I face?

You wont face any problem as such for now. See they dont verify this for the exam. So go ahead and prepare well and write.

During admissions, they will verify. You can explain then that you made a mistake. I suggest you also write to jeemain@nic.in explaining the problem. I dont forsee any problem as this can be dealt with during the document verification.

The problem areas are state code of eligibility, nationality and category. Mistakes in these areas will lead to problems. However student who have made mistakes in these areas also are not debarred unless its a deliberate attempt. They will be allotted seats after rectifying the details depending upon their new eligibility.