Kening, if you are appearing for NEET either as a Foreign National or NRI or an OCI, your passport and Aadhar card are 2 valid documents that you can show as proof. So even if your passport has an error in the name, showing your Aadhar card should be fine. But if you do not have an Aadhar card, then it might be a problem. Now the exam is 2 months away and if you can get the name corrected in your Passport meanwhile, everything would fall in place.

On the contrary, if you are talking about name on the passport size photo on the NEET application form, it is a matter of concern only if NTA has notified you and you didn't correct it. But if NTA has not notified it, you are absolutely fine. Please do let us know which passport is the issue so that we can help you with relevant information.