If an employee of a business purchases a cashiers check for the business of more than $3,000 and pays with cash from the business are we to record the business name as the purchaser on our MIL or should the employee conducting the transaction be recorded as the purchaser?

The person who is acutally puchasing the check.

Our logs allow for both to be recorded. Since this is BSA, you should know who the purchaser is as well as who the purchase is made on behalf of.

You are required to identify the individual who made the purhase. I do like the idea of logging who the purchase was made for. That could help later.