Sure. When you register on the website, you can enter both, a private and a business address, and choose which billing address you want to use before each trip.
You can - and should ;-) - connect your payment method with according billing address. This can be done by navigating to "My Account" -> "Addresses" and chosing the small credit card icon!
You can also change your personal data later in the login area of the website or app.