Yes, you can!
The best way to do this will be to add the other business as a new business on your Paystack account. To add a business, go to the top left corner of your Paystack Dashboard, and click the dropdown arrow beside your business name.
You will see an option to "Add a Business".
Here's a quick illustration:
This allows you to have separated transaction information and allows you to have granular settings over each of the different businesses on each website. In this case, you can use the same documents and bank account information to create each of these new businesses.