PETERSBURG, Alaska—For months, the tale of “Decoy Dan”—a local retired teacher running against a U.S. senator who shares his name—drew chuckles and eye rolls across this remote fishing village ringed by mountains.

Then, last week, Dan J. Sullivan Jr. was spotted catching a flight out of the tiny local airport. Next came the FBI agents knocking on front doors.

“Now it is serious,” said Susan Burrell, owner of The 420, a marijuana shop on North Nordic Drive, Petersburg’s main drag. “We don’t want to be known for the Dan Sullivan thing. We want to be known because we’re a great Norwegian fishing village.”For now, though, in a rainy borough reachable only by plane or boat, the double-Dan debacle is all anyone can think about.

The intrigue exploded after the New York Times reported that Democratic Party operatives helped to add Dan J. Sullivan to the ballot as a spoiler against Alaska’s incumbent Republican Sen. Dan S. Sullivan. Federal and state authorities are investigating, and President Trump said at a rally that the Democratic candidate Mary Peltola should be “prosecuted” and removed from the ballot.

Peltola told supporters Friday night that she was “deeply offended” by allegations that she was involved in an effort to recruit a namesake candidate. A federal judge on Sunday threw out a bid from the Trump administration to block state officials from certifying results if the incumbent loses. The joke has worn thin far beyond the village.

“It’s dirty pool,” said Alex Ziegler, an auto mechanic waiting in a line of more than 100 people at an early-voting location inside an Anchorage mall. Ziegler, a conservative who plans to volunteer as a poll watcher for the incumbent on Nov. 3, worries the dual Dans will confuse voters in a race he expects, “unfortunately,” to be close.

But Kelly Whitworth, a nurse in Anchorage, wasn’t buying the confusion argument. “People are smart,” she said. “They’ll figure it out.”She doesn’t always vote for Democrats, she said, but would this year. “I’m so disgusted with our current administration that I’ll do anything to get them out,” she added.

Sen. Dan S. Sullivan, for his part, leaned in to the saga on Halloween night, when he stopped by a trunk-or-treat event outside the Lions Recreation Center in Big Lake, about an hour north of Anchorage in the more conservative Matanuska-Susitna Valley.

Dressed in a ball cap, jeans and a Carhartt jacket, he quipped to one attendee that there he was going as “the real Dan” for Halloween. Along with candy and tote bags, he distributed navy-blue rubber bracelets printed with his name as it appears on the ballot: “Sullivan, Dan S. (Registered Republican) Incumbent.”

Back in Petersburg, nearly 700 miles by plane from Anchorage, the jolt of national politics has felt especially strange. This is a place better known for commercial fishing, where the fall moose harvest makes top news.

“We’re not exactly the center of politics here in the islands,” said State Sen. Bert Stedman, a Sitka resident who represents the area. He, too, wondered where the Petersburg Sullivan had gone. “If you were a legitimate candidate, which I’ve never thought he is or has been, that’d be the last thing you would do coming up to election day is disappear.”

In town, Grant Trask, a retired fisherman in a hooded sweatshirt, was scrubbing potatoes he dug up from the garden of the bed-and-breakfast he runs with his wife.

“It was a less-than-well-thought-out idea for him to put his name in for U.S. Senate,” Trask said. “Now, it’s falling apart. I feel sorry for him.”

In September, Dan J. Sullivan told the Journal that nobody put him up to running. On Sunday, no one answered the door of his barn-shaped house outside of town.

Meanwhile, FBI agents have contacted at least three of the local Sullivan’s donors, among them Charles “Rocky” Flint, the retired owner of a boat dealership who has known him for years, admires him, and offered $500 to his campaign when he learned he was running.

“I haven’t done anything wrong,” Flint said Saturday at his dining-room table, beside a large window overlooking open water and mountains stretching to the Canadian border.

He called the fuss mostly a late-campaign diversion tactic. “That’s what this current administration seems to be all about. Let’s create a shiny object over here, and then another one over there.”