(FORTUNE Magazine) – Starting later this year, you may notice some strange-looking names on the Web. Maybe you'll visit a site that ends with .firm or .store instead of .com, or perhaps you will write an E-mail to joe.netuser@mail.box. There's a lot of demand for these new names because a business name is a brand, and companies believe that so many of the good .com names are already taken. (For example, Delta.com is not Delta Air Lines; it's a small technology firm. You need to go to Delta-Air.com for the airline.)

You'll see the new domain names (as they're called), and you'll think, "How nice." But those small changes will be the result of a complex and often bitter struggle involving a cast of characters that would do justice to an Oliver Stone film. The players: a crowd of libertarian-leaning techies, a corporation with a government-granted monopoly, a cyberterrorist on the lam, and, of all people, Ira Magaziner, the notorious wonk and a chief perpetrator of the Clinton health-care debacle.

In the past the government funded the Internet, but now that business is a big presence, Washington can't bow out fast enough. The problem is, no one knows who should make the rules that hold the Net together. Those harmless-looking domain names have become a lightning rod for a heated debate--who should run the Net?

Governance has become a problem because the Net was never set up for business. Originally, most people on the Internet were academics, working under contract with the federal government. Informality was the rule; the spirit of mutual trust was such that individuals were often responsible for key network functions.

For example, a single person, one Jon Postel, has traditionally overseen the crucial address lists that tell each machine where every other machine is. Postel, one of the original Internet engineers, wears socks under his sandals and has a long grizzled beard and a ponytail clipped with a barrette. For 20 years he has been an employee of the Information Sciences Institute at the University of Southern California. But his most important job is control of the little black book of addresses that enables the Internet to work.

The Internet old guard trusted Postel and the Internet Assigned Numbers Authority, as he called his address maintenance function. But as companies began to wise up to the Net's moneymaking potential, some began to have doubts about the arrangement. Billions of dollars were expected to change hands over the Internet. How could one man, Postel, with no legal framework set up around him and no accountability, be so key to the Internet's stability? One technology writer compared Postel to the Godfather; The Economist shortened that to "God."

The power vested in one hirsute engineer, the new business pressures, and the resistance of the Internet's old guard to change were potent ingredients for a power struggle. All that was missing was a spark to set it off. Enter domain names, another relic of the old Internet. The domain-name registry system for .com, .org, and .net addresses in the U.S. has been controlled since 1993 by a Virginia company called Network Solutions through a "cooperative agreement" with the National Science Foundation.

At first, no one cared that Network Solutions had an exclusive. Only about 2,000 businesses had registered .com names, and they had done it for free, thanks to taxpayer support. But on today's capitalist Internet, Network Solutions was suddenly sitting on a gold mine. Loath to subsidize business addresses, the NSF had stopped funding .com names in 1995, authorizing Network Solutions to charge $100 for sign-ups. Despite the cost, the registrations have poured in. There are now around 1.5 million.

Network Solutions' monopoly isn't just a matter of bits and bytes; domain names have become a pop culture phenomenon. They're ubiquitous--.com addresses are on billboards, T-shirts, TV screens. In a hallway at Network Solutions, engineering vice president David Holtzman has mounted a stock ticker that flashes new names as they're grabbed up by customers. Many of the names are pedestrian--like www.thepetstore.com. But Holtzman says he's seen others like www.deadfatcomics.com, presumably a memorial to the comedian Chris Farley. "When Princess Di died," Holtzman says, "this thing was clogged up for weeks."

A lot of people decided they were aggrieved by Network Solutions' government-sanctioned monopoly. Trademark holders felt that the company didn't respect their concerns; Internet old-guard types disliked the idea of anything on the Net being for sale; entrepreneurs were angry that they couldn't get a piece of the expanding .com licensing business. A few self-starters tried to market new .com equivalents. (The most notorious alternative registry is AlterNIC. To attract traffic to the site in July 1997, or perhaps to protest Network Solutions' monopoly, co-founder Eugene Kashpureff allegedly hacked into Network Solutions' site and diverted some of its hits to AlterNIC. He settled with the company but then fled to Canada, was arrested, and is awaiting trial.) But new registries have not been able to establish new domain names on the Net because they don't have access to the key address information--only Postel, Network Solutions, and the government have had access to this information. At least one would-be registry has sued Network Solutions and the NSF to get to the computer file it needs.

The only alternative naming service that did appear to have an inside track to that address file was one proposed by the Internet International Ad Hoc Committee (IAHC), founded by Postel and other Net old-timers. The IAHC's plan recommended seven new domain names as well as a system of new registries. In May 1997 the NSF announced that it would not renew its exclusive agreement with Network Solutions. On July 1 the Clinton Administration released an electronic-commerce initiative aimed at turning the Internet--including domain-name registration--over to the private sector. Authorities thought that the IAHC plan might be the solution.

But when the Commerce Department and Congress asked for public input into the domain-name matter last summer, they were stunned by the number of complaints. Critics accused IAHC of being out of touch with the new, business-oriented Net community growing up around it. By December 1997 all sides were deadlocked.

With the conflict now a crisis, whom did the White House decide to call? Ira Magaziner. "It became clear things weren't evolving properly," says Magaziner, who was one of the architects of the President's electronic-commerce initiative. Yet, despite his reputation as an icon of big government, the domain-name combatants are all coos when it comes to Magaziner. "He's very good about listening," says Postel. "I applaud him for his methods and energy," says Donald Telage, a senior vice president at Network Solutions. Magaziner plugs away earnestly, borrowing from his health-care playbook. He sits in meeting after meeting, all in the service of a workable domain-name compromise. He has talked to more than 100 "stakeholders" in just the past six weeks.

Magaziner's plan has missed its Jan. 15 deadline, but everyone seems willing to cut him some slack. Most expect Magaziner to call for the creation of a private, nonprofit international Internet governance body, with a board of directors, to take over Jon Postel's address-minding authority. Business people will have a place in the new organization, which will probably be based in the U.S. Postel will be onboard too. "Jon Postel is important," says Magaziner. "The legitimacy he provides, the historical connection he provides." Registrations will open up to competition, but there'll probably be only a few business alternatives to the .com suffix.

When the new structure is in place--if the plans pan out--the issue of "who runs the Net" should be resolved. Ironically, all the Sturm und Drang, at least as far as domain names are concerned, may have been for naught. Most experts expect new technology to make domain names obsolete. "There's a great business opportunity for a really good directory system," says Postel. "If it worked well, you wouldn't need a .com at all."

INSIDE: Cool company: Tribune Co., page 126... Above the Crowd, page 128... Great tool for the paranoid, page 129... Alsop wires his digital manor, page 133