Under the Addresses tab in Maintain Vendors you should be able to add up to 20 ship-to addresses.

The first name is the Billing address.  You must add a contact name for each shipping address.   Add New Contact and enter the address. 

Yes, I was not thinking.  Vendors do not have Ship-to addresses, they have Remit-to addresses.  So this question must be about customers, not vendors.

Technically speaking, It is the same for both vendors and customers.  You need a contact name for each vendor or customer address.  The concept is still the same.