How do you handle if when a customer is bought by another Company? Do you rename the account to the new name? Or do you create a new account?

How do you handle if when a customer is bought by another Company? Do you rename the account to the new name? Or do you create a new account?

At times I've felt like renaming the account, its easier, but something tells me that I should create a new account and move any contacts from the old to the new one. old Sales Orders should remain with the old account and the new account should start building its own history.  Anyone has any input in this?