Correcting date of birth on L1 visa

[gkp1976]

I am victim of the typical case of Date of birth mismatch in birth certificate and all other documents. I plan to get the DOB corrected in passport as per the birth certificate.

1. Do I need to get the DOB corrected in L1 visa as well?

2. What is the process for the same?

Appreciate your time,

GP