Yes, it can if you are considering Short Service Commission exams or any Government Job.
Such mistakes are seen often by candidates while applying for higher education or for a Job.
Please check your other documents like Aadhaar Card, Voters card, Driving license and other certificates for spelling mistakes related to your name and mother's name
Please check father's name in his Aadhaar card and other documents.
Make an affidavit via a Notary who can guide you with the name correction affidavit to be issued in legal terms.
Then publish the correct name in an English paper and a vernacular language and preserve both the original paper publications.
The approach the school you have studied with the above documents along with your original marks card. The school prinicipal will forward the application to the 10th board and you can get the correction done. If your school (10th standard) is nearby you can approach the school office administrative clerks or exam in charge, they can guide you as they will be familiar with the local policies too.