Never an issue of photo, you can go in FAQ section that is provided in NEET's site they it is clearly mentioned that students uploading photos without name and date have no issues however on the correction date if they permit to change the uploaded photo try to change that to be on a safer side.
It is a common error done by the applicants. You are not alone in the category. CBSE is aware of these things. Your application will be accepted with out any hassle. It is time to concentrate on your study. Best of luck.
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