(FORTUNE Magazine) – Unless you've been down a deep, deep hole, you've no doubt heard about the Y2K problem, the world's biggest computer programming boo-boo. But hundreds of companies are dealing with a more prosaic Y2K problem: Somewhere in their name is the soon-to-be-musty phrase "20th century." Corporations as diverse as 20th-Century Breeders (artificial insemination of animals) and Twentieth Century Fox (commercial entertainment of people) are staring into the not-so-distant future, and they don't like what they see. Come the stroke of midnight just a short 17 months from now--or 29 months, depending on how you count your centuries--a name that once sounded impressively up to date is gonna be about as cutting edge as "Betamax."

Everyone agrees you can't just let it slide: People don't want to wake up one morning and find themselves riding an iron horse when everyone else is zooming by on personal orbital craft. As Judy Pendergrass of Judy's 20th-Century Hair in Grants Pass, Ore., puts it, "Golly, you gotta change your name."

Few companies are taking advantage of the name change to get creative: Mutual fund titan Twentieth Century has rechristened itself American Century; the think tank 20th-Century Fund went for the generic Century Foundation; Gateway 2000 is excising the 2000 from its name.

But even little changes aren't cheap. It cost 21st-Century Collision in New Windsor, N.Y.--a mere speck of plankton in the ocean of American business--$2,500 to change its name from 20th-Century Towing & Autobody. Think what the tab will be at a company the size of Twentieth Century Fox. Assuming, that is, that Fox even deems it necessary to change. Taking the paranoia of its hit movie The X-Files to extremes, Fox is having a tough time acknowledging there might be a problem. When FORTUNE called to inquire about this impending nomenclatorial dilemma, an edgy Fox functionary replied, "I really can't talk about it, not on the record."

And then there's a special case: Will a certain real estate firm that's managed to stay one step ahead of the game try to dart ahead again? Century 22, anyone?

--Steve Casimiro