Business Units are an add-on feature in HubSpot used to manage multiple brands in one HubSpot account.
One thing to consider when switching out one business for another in a business unit is that the forms cannot be re-assigned to another business unit like you can with properties and contacts. That means that if you rename this business unit, you'll have the old business' forms associated with the new business.
If you don't want that to be the case, you can either re-make the old forms in another business unit, or you can delete the business unit. The account will disappear but the data associated with it won't get deleted.
When you rename the unit, you'll want to swap the brand kit, the integrations, and the properties.
If you swap the properties to another business unit, it's still the same properties and the historic record data will be in that property. So if you want to separate historic data in a clean way, just create new properties.
Here's a HubSpot article about managing Business Units for any further clarification needed.