Since your name and the parents name are correct, then there should not be much issues.
When you apply for passport, visa and travel in future on official duties or overseas banking job, then the surname of your parents become important.
When you have time, it would be better to change the certificates.
You can either apply for a correction service to the boards or approach the 10th and 12th board and apply for duplicate certificates.
You would the marks sheet 10th, 12th, the school certificates, documents that have your parent's full name (ration card, PAN card of father and mother), payment of the prescribed fees.
With the above, forward a letter requesting the service to the 10th and 12th board via the respective school/college prinicipal.
It would take around 4 weeks for the corrected new certificates to be despatched back to the appropriate school/college. You can collect it from them.
For the B.Tech, you can follow the same procedure by contacting the respective university office either by post or online if the service is offered.
In the meanwhile, if you are up for document verification, keep your parents original Aadhar card/PAN or Ration card that has their full name so that you can explain to the authorities, they would oblige as it is not a major mistake or a mistake in the candidate's (your) name.