Yes you may face some problem so inform the heads before only or right a mail to them that will look for your issue you have to submit the proper documents with your name without any mistake and you may have to sign grievance letter for the mistake in your name 

Hey Ashish,

I suggest you call their helpline so that they can guide you through the process. Name in the application is very important and crucial. Or better to go for the counseling, the computer operator may help you. And when you go there it's better to take some proofs with you so that you can prove that it is you who applied for the exam. Like aadhaar card, class 10 admit card and result. 

usually, there is a correction window after applying the form. But as its been late I suggest you to follow the above options. 

Head Office:

8th Floor, 

New Excelsior Building, 

A. K. Nayak Marg, Fort,

Mumbai – 400 001, (MS)

helpline no. : +91-22-49150801