By default, each contact will be the 'Bill To' contact when you are viewing your unbilled items. This can be changed within the contact's details under the basics section.

If you need a single work item to be billed under a different contact, perhaps when the contact is billed as an organization, you are able to change the 'Bill To' contact within the work item. This change is made in the Billing section on the Details tab of the individual work item.

You can also individually change the 'Bill To' contact within the Unbilled section of Billing. Click on the work item that you'd like to change the bill to > use the options menu (...) on the right and choose 'Change Bill To'.