Hello,

You should write the correct details in the NEET exam OMR and you can verify your identity at the time of counseling by showing respective ID proofs.(it won't be a problem until you have all the original documents needed).

Also during the examination do carry accepted Identity cards (school ID,  aadhar card, pan card etc) to avoid any confusion at the exam center.

Don't worry much focus on your exam,  it won't be a issue.

Hope this helps