It's called a "Tag Line" or "Lure Line" which is quite common in all industries. Doug Henning used one that read "Magician for Hire: Have Rabbit Will Travel"
When I work mixers I wear a button that says, "Read My Mind"
There's dozens of examples, some offering a very droll pun (such as the original tag line noted in this thread) while others go for the "cute" (like the Henning ad).
Though I'm no longer doing traditional magic there was a time when I really could use that tag line and deliver exactly what I promise in the ad. Think about it YOU REALLY CAN SAW SOMEONE'S WIFE (OR HUBBY) IN HALF, there's at least a half-dozen variations to the Sawing that range in price from as little as $100.00 to a high of about $8,000.00; those that pack in a suit-case to those that require a mini-van to transport. So it's plausible to get work via this offer or to offer to make one's In-Laws (or Boss) Vanish and so the list goes on.
In Mentalism there is a famous script penned by Carl Herron (Bro. Shadow) entitled "Have Seance Will Travel" which is the tag line he used in the local paper to promote his private sense shows (if you think like a magician you will be highly disappointed in this program; it's not full of tricks but pure psychology). It's a very commercial program because of the tag line; people call just to see what his service is about just as they do when they see headers in ads like the about.