IN HOLLYWOOD, WHERE HE WALKS TALL IN ostrich cowboy boots and wears a 10-gallon hat, Wyatt Earp has learned that introducing himself can be perilous. "Oh, yeah?" said one woman upon meeting Earp, namesake and descendant of the legendary lawman, "and I'm Calamity Jane."

But now that Kevin Costner's Wyatt Earp has hit the theaters, today's 6'4" Earp hopes to soon reap some of the marquee value for himself. The 31-year-old fledgling actor and banker (his business card reads "Wyatt Earp, Senior Loan Consultant") plays a bad guy in 1993's Tombstone, a film about the Earp legend that is now in video stores. "Look him in the eye," says Tombstone costar Sam Elliott, "and you know he's not a joke."

Raised in Perkins, Okla., Wyatt traces his ancestry to Joshua Earp, the great-grandfather of Tombstone's famous lawman. The youngest of four children born to oil wildcatter Lee Earp and his wife, Wanda, Wyatt earned his spurs wrangling cattle as a boy. After graduating from Oklahoma State University, name recognition helped him become, at 21, the youngest Republican chairman in the state and later a real estate and oil broker. In 1988, Earp pulled up stakes and moved to L.A. to become an actor. "I was bored," he says. "I wanted to get the hell out of Dodge."

After several fallow years, Earp landed his small part in Tombstone. A family-history buff, he says his celebrated ancestor laid down his badge in 1882 and eventually moved to Hollywood. Cowboy stars Tom Mix and William S. Hart would serve as pallbearers at the lawman's 1929 funeral.

Now hoping to appear in more films, Earp, who lives in a Santa Monica condo and courts Oklahoma City psychologist Brynda Wheeler by phone, recalls lean days when a former agent begged him to change his name to anything but Wyatt. "People thought it was a gimmick," he explains. "But I was real."