By BRAD STONE


SAN FRANCISCO - Since Facebook started giving out customized Web addresses like face book.com/ yourname in June, more than 9.5 million people have rushed to grab their top choice.

On Twitter, public fights have broken out over so-called impostor accounts.

Celebrities, companies and even regular people can be excused for feeling a bit of deja vu. Staking out and protecting their names and trademarks on the Internet has become a seemingly never-ending battle.

When domain names first became hot properties in the ‘90s, it was mostly companies that worried about claiming the right addresses. But in this more narcissistic Internet era, people who were once happily anonymous view themselves as online mini celebrities with their own brands to promote.

Those whose names are not unique may run into problems in trying to manage those brands. Chris Hardwick, a stand-up comedian and host on the tech-focused cable network G4, had no trouble registering chrishardwick.com a few years ago and securing the appropriate Gmail address. But he missed out on claiming his name on MySpace to a Chris Hardwick in Ohio. Mr. Hardwick got home from a performance too late to get his address of choice on Face book; he said a high school student in England appeared to have grabbed it.

“It’s like a Wild West town full of Chris Hardwicks with their hands on their mouses getting ready to draw on each other,” he said.

To some, the rules of this new game are frustratingly hazy. Facebook has invited trademark holders and celebrities who find their names are taken to fill out a complaint form on the site. It says it will resolve disputes on a case-by-case basis. Twitter has begun verifying the identities of well-known users, giving them a badge on their pages that serves to confirm that they are who they say they are. A Twitter spokeswoman, Jenna Sampson, said the program was a small-scale test at this point.

No one knows whether any of this online terrain has any lasting value - only that accounts on sites like Twitter and Face book tend to show up at the top of the list when people search the Web. So many people are plunging in - including so-called cybersquatters who hope to profit from Web addresses and accounts.

Social media sites give companies new ways to promote their brands, said Howard H. Weller, a trademark lawyer at Mitchell Silberberg & Knupp in New York. But he added that “these are all new avenues for abuse, and it’s more resources trademark owners need to devote to policing and enforcement.”

For example, Dell grabbed facebook. com/dell, but Jeremy Fancher, a student at Washington University in St. Louis, registered facebook. com/dellcomputer and plans to try to sell it. A Dell spokesman declined to comment.

“I think it would be sort of funny if another computer company buys it,” Mr. Fancher said. “It all illustrates how murky the water is when signing up for these accounts.”