Can I bill a business instead of an individual?

You bet! 

To bill a business so that the company name shows up accurately on the invoice, you will first want to set up a person within the business -- e.g. the owner, CEO, etc. -- as the "primary" client under the First Name and Last Name fields. (This ensures that you can receive a legal signature for an individual representing the company if you send out contracts via the eSignature integration.)

You will then designate the exact business name to display on the invoices themselves -- this can be done when first adding the client or by editing their Profile:

The resulting invoice PDF will look like this: