Yes, you can set “more than one” shipping address to one customer. Steps are same as you add address for customers, just select “Shipping” under address type. But make sure you are not selecting the “default address”.
Obviously, if you will be loading each “ship to address” for a particular customer, you can track the “Delivery” based on customer and “ship to address” basis.
Is there any way to create those custom address titles in the GUI or is this something that can only be done via import?
When I am in the customer screen and try to add an address, the system seems to only allow me to select from the default address titles but there is no option to create a custom title.