It’s the height of annoyance to wear a dress to a special party, only to have two other women arrive wearing the exact same thing. Even more irritating might be getting elected to Congress and then having two guys with the same name show up, too.

[IMGCAP(1)]That could happen to Rep. Mike Thompson. The California Democrat faces the prospect of having two colleagues named Mike Thompson after the 2010 elections.

Both of the “other Mikes— are state Representatives who might enter GOP primaries in Republican-leaning districts. Both are vying for open seats created by Members leaving to run for governor of their respective states.

The Oklahoma Thompson is considering a run to replace Rep. Mary Fallin (R), while the South Carolina Thompson is among those eyeing the seat Rep. Gresham Barrett (R) will leave.

If that wasn’t confusing enough, just wait until they’re all in Congress and sponsor a Thompson-Thompson-Thompson bill. Just when we finally managed to tell the Udalls apart …

“I’m sure they’re all good guys,— Oklahoma Mike told us of his fellow M.T.s. And what, we had to ask, made him so sure of that? Seems there’s some kind of positive karma attached to the moniker.

Thompson told us that when he first ran for office, he knocked on a lot of voters’ doors. “And lots of people had known a Mike Thompson’ in their lives,— he said. “And they all said that the Mike Thompsons they knew were good guys.—

The South Carolina Thompson offered HOH two ways to distinguish him from his potential future colleagues: A) he has a strong Southern drawl, and B) most people call him “Michael,— not “Mike.—

Michael-not-Mike said he’s taken note of the Congressman with whom he shares a name — in fact, the California Democrat might have unwittingly fueled the South Carolinian’s political ambitions: The Palmetto State native once visited Washington, D.C., and happened upon the California Democrat’s office. “I took a picture of that name plate and used it as my screensaver for a while,— he confessed.

But a spokeswoman for the Congressman said her boss isn’t losing sleep about the would-be competition. “He’s urged everyone not to count their Mikes before they’re hatched,— she told HOH.

Or elected.

A Speaker and a Gentleman. Speaker Nancy Pelosi is attracting Hollywood’s leading men these days.

Fresh off her date (OK, so it was a business meeting) with hunky actor Brad Pitt — who came to Capitol Hill on Thursday to lobby on New Orleans housing — the California Democrat spent her Monday with debonair actor Richard Gere.

Gere is chairman of the board of the International Campaign for Tibet and was on Capitol Hill to mark the 50th anniversary of the Tibetan uprising and the Dalai Lama’s escape into exile. The actor chatted with the Speaker about the situation in Tibet, focusing on border issues and the hundreds of people who have been imprisoned there for peaceful protest, ICT spokesman Ben Carrdus told HOH.

Gere and Pelosi (a staunch critic of China’s treatment toward Tibet) are old pals, having met up on Capitol Hill several times over the years. Gere cheered on the Speaker during her swearing-in ceremony at the Capitol back in January 2007. And when Pelosi awarded the Dalai Lama with the Congressional Gold Medal later that year, Gere was among the invited guests.

Pelosi isn’t Gere’s only Capitol Hill contact — the silver-tressed actor also visited with Sen. John McCain (R-Ariz.) and Rep. Ileana Ros-Lehtinen (R-Fla.) on Monday, Carrdus added.

Still, you can’t keep best friends apart: Pelosi and Gere were set to reunite at an evening reception in the Cannon Caucus Room.

Senators Reach a New Low (as in Juliette). Girl Scouts often learn about campfire-building and knot-tying — and don’t even get those chicks started on cookie-salesmanship. Now the badge-collecting girls are about to get schooled in another subject: the women of the Senate.

Home-shopping channel QVC is donating 25,000 copies of “14 Women,— the 2007 documentary about the women serving in the chamber in the 109th Congress. Reps say the gift, which honors the March 8 International Women’s Day holiday, will help inspire young women to become leaders in their own right.

Narrated by actress Annette Bening, directed by Mary Lambert (sister of Arkansas Democratic Sen. Blanche Lincoln) and produced by Nicole Boxer (daughter of California Democratic Sen. Barbara Boxer), the movie chronicles the struggles and triumphs of female Senators — whose ranks have now swelled to a new record of 17.

“14 Women— “gives us an inspiring and timely new way to help fulfill the leadership mission that has sustained Girl Scouting for 97 years,— Laurie Westley, senior vice president of Girl Scouts of the USA, said in a statement.

We’re just hoping that “leadership mission— continues to involve plenty of Thin Mints.

State of the Art. Tourists weren’t the only ones taking advantage of the warm weekend weather to stroll the Mall and ogle some art. An HOH tipster spotted Sen. Lamar Alexander and his wife, Honey, taking in the “Pompeii and the Roman Villa— exhibition at the National Gallery of Art on Saturday.

According to our tipster, the Tennessee Republican blended right in with the sightseers, sporting a polo shirt, khakis and an orange baseball cap (perhaps in support of his home-state Tennessee Volunteers).

“I couldn’t help but find it ironic that a place that used to attract Senators (of the Roman persuasion) still attracts them to this day,— our history buff/tipster joked.

Lauren W. Whittington contributed to this report.

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