If your mothers name is written on  NEET 2019 Admit Card, then do not worry just send a mail to - neetug.nta@gov.in. You need to mention NEET Admit Card in subject section and mention your issue in the text area.

But you have must done this before as now there is no time left. I will suggest you to go with your id proof and admit card. It depends on exam centre and invigilator whether they are going to allow you to sit examination or not.

Good luck.