Hello,

You can do one thing you will carry the same name of your mother which including your 10th and 12th marksheets.

Another thing you can do, that is when NEET result will publish and you get any college due to counselling then you can apply an affidavit for your mother's name in 1st class magistrate and use your mother's real name in your college. After admission you can apply for correction of 10th and 12th marksheet in your passout school board website.

All the best.