As per your doubt, you will have a problem in future not only in government job but also in any other jobs. If the surname is mistaken then it won't be a problem but the name itself having mistake will create a problem. Suppose if you're a student you have time to change your name. Otherwise, if you have applied for any job and waiting for the interview and worried about the name then you can make affidavit of your name for temporary procedures.
If not in a hurry then you can write a letter to the board stating that there was a mistake in your name and you request to correct it. Along with the letter attach a xerox copy of the documents which you need to produce with attestation of an officer. You apply it online also to the board.
This will take time for completion, meanwhile, if you need to submit your marks card to any organization then you get an affidavit along with legal advice. To know more about this check for the previous same type of queries in ISC which are answered by experts.