The probability of facing any problem regarding the wrong name under your Photo is very less. So you have nothing to worry about it and if it is asked you have your other details through which you can surely clarify your name. So don't worry about this. Also the 10th certificate is asked only for the DOB purpose.

The documents that are required for the NEET counselling are provided below:

• NEET Admit Card

• NEET Scorecard or Rank Letter

• Class 10 certificate and mark sheet (for date of birth)

• Class 12 certificate and mark sheet

  Recommended

• ID proof (Aadhar/PAN Card/Driving License/Passport)

• Eight passport size photographs

• Provisional Allotment Letter

• Caste Certificate (if applicable)

• PwD Certificate (if applicable)

NRI/ OCI candidates appearing for Deemed Universities must submit the following documents

• Passport copy of sponsored, embassy certificate
• Sponsorship affidavit (stating that sponsorer is ready to bear the expenses for the whole duration of study)
• Relationship Affidavit (Relation of Candidate with the sponsorer)

To know more about NEET Counselling visit the link below:

https://medicine.careers360.com/articles/neet-counselling

I hope this answer helps. All the very best for your future endeavors!