That is a horrible thing to have happen.
First, I believe that you were sexually harassed. Sexual harassment can be used to define an employee asking out a customer while on the clock at their place of work. Outside of work, this may have been absolutely OK, but on the clock, NO!!
To all of the people who are justifying this, What are you thinking?!?! Imagine if your UPS driver invited to hang out and smoke after his shift. I would be livid, and I bet you would be too.

Secondly, it is absolutely ridiculous that he responded in such a fashion. I know for a fact, the driver does need your name in some instances. I process deliveries where I work, and the driver need my last name and signature for delivery records.
A professional driver would have seen the customers confusion, and responded with "I'll pass on providing that, however we need your name for delivery records information"