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Need some guidance on how to proceed. I made a mistake on one of my CVs during OCI applications and used the name of another firm in the CV. Still got the interview. I feel embarrassed. How should I proceed?

I was thinking of taking a new CV and giving it to the interviewer during the interview.

If you have something else that is significant and updated on your resume then I'd use that as an excuse. Otherwise, I would say nothing unless they bring it up (which they almost certainly will not if you got the interview).