This idea combines the fact that people our willing to pay to get their name in print (vanity publishing) with the fact that movie studios are already willing to let companies pay for product placement. To make it work a production company or studio would offer a new product - people placement (names) in movies. Some of the details involved are listed below.
1. People would be charged an amount based on how big they wanted their name to appear on the screen. For instance, a name on the list of names an actor looks at on the call box outside of an apartment building would cost just a little, a poster advertising a new perfume in a subway station would cost more, an advertisement for the Wonderful World of Widgets on the side of a bus would cost even more, and at the top of the line you could up a billboard for John Doe's Pet Shop and Wholesale Meat Company.
2. The price of these people placements would be high enough to take care of whatever it cost to produce the actual display plus a reasonable margin.
3. Buyers would be able to pick the genre they want the name to appear in so if a guy was buying it as a gift for his girlfriend he could make sure her name showed up in a romantic movie and not a horror movie.
4. Allowances would made for deleted scenes. This could be handled by moving a name that's been used to the bottom of the waiting list and only dropping it off when it actually appears in a movie. If the scene the name was in gets deleted during editing then that name would move back up to the top of the list to make sure it made it to the big screen.