"Now that I look at this, maybe the customer put in a business name."
yes, it looks like they did not enter both first and last names.
"and add that item to the cart, shipping is not showing up and if they click the PayPal Express it does not carry over shipping."
With paypal express the shipping is not calculated until the user goes through paypal to set the shipping and billing address, and is then redirected to the pp_confirm page
on the pp_confirm page, the shipping is calculated and the user can cancel or confirm the transaction.
this is as designed.