Users will have the dropdown list of address and location but should have and Edit link so the users can customize the shipping address or edit/add shipping names from the checkout page. Users now have to leave the checkout page and go into their account to modify the address. If users can do it from the checkout page, that would be perfect.
I would like to upvote this. It is extremely unintuitive that the customer must select a shipping method way upstream before they even get to their shopping cart. I can't think of a single other e-commerce site that works this way. If you insist on forcing the customer to do this which browsing products, then at the very least give them a way to easily change it during checkout. Otherwise you're contributing to shopping cart abandonment.