One method: You can run multiple web sites through one PayPal Business Account however, there are limitations. One method that works well for many online businesses is to have a business name that does not associate you with any specific web site.
For example, your business name could be Acme Limited. This is the name that would show up on customer's transactions even if they purchased from John's Mower Parts or Mary's Handbags.
You can customize each web site with a different business graphic logo but, because, you are limited to one PayPal Business or Premier Account, your actual business name needs to be neutral.
It's also a good idea to explain to your customers that when they see their statement, the billing compay, Acme Limited, is the parent company of John's Mower Parts or Mary's Handbags.
Another method: If you have two separate companies with different sets of accounting books and different business bank accounts and/or credit cards, you can have two separate PayPal accounts.
And another option if you use Website Payments Pro. There is an option to have "Child Accounts". It's not something you can setup yourself, it must done by PayPal. You must contact PayPal's Customer Service for assistance.