See technically if your result is great and the information you will enter during the counselling is similar then you will not face any problems. Now if you have the name of your mother different in 12 marksheet then technically your 12 marksheet then its better for you to have a Gazetted officer verified attested copy. If any problem arises you can show it as an reference. The second solution can be that you can rectify your marksheet as per the procedures as prescribed by your boards which you can get the full info from your school office.

I hope this answer helps. All the very best for your future endeavors!