hi,
The Name is not a required field for the custom entity "Address" hence is not present. You can add it by going to Settings -> Customizations -> Customize the System -> From the Entity list select the Address that you are interested in (note: there
are 2 listed) -> Forms -> double click the Form to open the form editor -> you will see Name in the Field explorer -> double click/drag & drop it where you want it -> save - Publish the form and you should have it :)
The one that you see on the Constituent form is the Primary address I believe. There is no way to mark any one of the addresses from the list as the primary.
thanks,
RBaliga