NEET registration parents name error

That will not be an issue. There is no mistake in the name. You have written the full names of your parents as per their Aadhar cards. Your marks lists will have a short form of the names only. But nobody will object to that. In case of any doubt, they may ask you to bring the copies of the Aadhar cards of your father and mother and verify. When they match no issue will be raised. Don't think about that and focus more on your preparation for the examinations so that you will get a good rank in the entrance test. All the best.

It is always better to be consistent in names, date of birth, and other credentials in respect of self as well as parents because that creates a problem at a later stage, especially at the time of document verification. Anyway in this case the variation is of minor nature and can be supported well by presenting the Aadhar card of the parents where their full name is mentioned. You have also mentioned the same in filling out the NEET form. Please take the original documents along with the parent's Aadhar card so that at the time of document verification you can clarify the variations between the names in various documents. So, I do not see any difficulty in this case for you to be encountered at the time of document verification.

While writing details in application form you should be alert. As you know that personal details especially name error sometimes create problem at the time of document verification. But in your case, you need not to be worried. As told by you that you have written parents full name in NEET form so there would not be problem. For better clarification you bring parent's aadhar card at time of document verification. Aadhar card is very important identity in today's date. As per my view, You should concentrate on examination instead of thinking this issue.

I don't think that you will face any issue relating to this minor issue since you have entered the full names of your parents. What they can do at best is to ensure the correctness of the names of your parents by getting these verified through their Aadhaar Cards. You need to take a cautious step of carrying their Aadhaar Cards along with NEET Admission form so that the verifying authorities would examine the correctness of your parental names.
What is needed from your end is to devote your full time to your ongoing studies so that your scorings in the said examination are impressive enough to get a good ranking enabling you to get a seat in a prestigious medical college.