A correspondent bank, which we do business with, and is currently listed on our BSA Exemption List, was acquired/merged in the last six months with another bank. My question is do we need to file a new initial Designation of Exempt Person reflecting this change?

To paraphrase Richard, the bank in question is exempt by its very nature. However, since you want to make sure your filings are complete, and avoid exam "gigs," file the Designation and keep a copy in file.