Dear Bright Baby,
You can ask Mommy to go and file a correction request at the Local Civil Registry (LCR) of the city where your birth was registered. Requirements usually depend on the case of error, like if a letter or a full name is wrong. The payment will also depend on the needed correction.
After the correction has been made, the LCR will endorse the corrected record to the NSO. This takes around 6+ months to accomplish but the earlier you ask Mommy to do this, the fewer problems you will have when you grow up. Remind Mommy to keep all the correction and filing receipts handy so that she can use them as references if needed.