Hello Aayushi! 

You have to get an Affidavit done from the court in which you have to mention that what is their real name and what is that name which is written in Neet form. Also there must be a statement that both these names belong to same person and they aren't different. This thing can be done in 1-2 days maximum depending upon your lawyer. 

Narrate entire thing before a lawyer and he will help you.

All the best!