Hi

You don't need to worry at all even if your Aadhaar card has mother's name and your father's name is there on the neet admit card , it's completely ok and you are all safe .

What matters is your name and your photo in your ID proof and  your father's and mother's name doesn't matter, they don't check it  while allowing you into the examination centre.

Also, along with the valid photo ID proof like aadhar card or PAN card etc you should carry following documents as well to you neet examination centre

* Printout of your NEET examination admit card

* Your  passport size photograph

*PWD certificate (if applicable)

For details go through

https://medicine.careers360.com/articles/neet-exam-day-guideline

Thankyou