Are surfers worried about what may appear on their CC statement when they sign up?
 

Are they?

Of course, you think they will like seeing BIGGAPINGASSHOLES.com on the cc bill versus ABC internet services?

what do program owners do to soothe their surfers fears?

:Graucho :Graucho :Graucho :Graucho

Tell them clearly on the join page how it will appear on their credit card statement and make it something that can be passed off a software or some other non-porn product.

You show them what the charges will appear as on their bill. Anybody with sense lists their company name, not a website. Also, listing your website (especially if it's explicit) in your corporation name is not suggested for many reasons. You don't want your mail or company checks made out to Gapingassholes.com anymore than a surfer wants to see it on their credit card bill.
Being discreet in that sense is both a smart personal and business move. Nosy people can fuck up a good thing.

usually they say something like such and such will appear discreatly on your credit card statement.