John Edwards and Carol Becker agree on at least one thing: “Wedge Live” is a pretty good name.

Over the past few days, questions over which person can legally use that name have generated vehement debate on social media over trademark law and neighborhood politics, and allegations that Becker — an elected official in Minneapolis — is trying to co-opt the moniker in attempt to silence her critics.

Edwards, a graphic designer, began using the title “Wedge Live” about four years ago to blog and tweet about politics in the Lowry Hill East neighborhood, commonly known as “The Wedge.” In what he calls a “full-time hobby,” Edwards has gained thousands of readers and Twitter followers for his often-satirical commentary on city political issues, with a focus on zoning and housing debates.

He said he’d never heard of Becker, a member of the Minneapolis Board of Estimate and Taxation, until she sued then-Mayor Betsy Hodges last year over the timing of her 2018 budget release. Edwards saw the lawsuit as a political stunt, he said, and decided to respond with a sort-of-joking, sort-of-making-a-point bid for her political seat.

Becker lost the lawsuit against Hodges. Edwards lost his write-in campaign.

Then, last week, a Wedge Live follower sent Edwards an image of a legal notice in the Star Tribune. It said Carol Becker was filing paperwork to conduct business under the name “WedgeLive.”

“I couldn’t believe it,” Edwards said. “It seemed like a very extreme thing to do … at that point, I didn’t know, am I about to lose my brand that I’ve built for four years?”

In an interview, Becker acknowledged she filed business and trademark applications to do business under the name. But she denied it was an attempt to silence Edwards.

Becker said she wants to start a national podcast that addresses divisive issues — or societal “wedge issues” — and thought “WedgeLive” would be an appropriate name. She said the blowback has been outsized.

“This has blown up into this, ‘Oh my God, Carol’s trying to shut down this website,’ ” she said. “It’s just kind of crazy. I’ve done nothing at this point, except file for something that I think I can maybe make money on as a business.”

Becker said she does not read Wedge Live and does not use Twitter. She’s aware of the blog, and knows Edwards is a critic, but said that had nothing to do with her choosing the name.

“I’m not out to get Mr. Edwards,” she said.

Edwards doesn’t believe it. He said that Becker has criticized his blog by name and sent him social media messages in the past asking to meet.

“It’s weird,” he said. “The lack of judgment that it shows on her part is strange. She can criticize me all she wants. She’s free to do that. But to try to take somebody’s platform away — I just think it shows really bad judgment, and that she’s really not fit to serve as an elected official in Minneapolis.”

After outrage on social media and a post by independent journalist Tony Webster, Becker said she filed to withdraw her applications for the name rights. But if no one files for it in six months, Becker said she may try again.

“They’re not a registered nonprofit,” she said of Edwards. “They’re not a registered lobbying group. They’re not a registered political action committee. They’re nothing. So, just because a group exists, doesn’t make it a legal entity.”

William McGeveran disagrees.

McGeveran, who teaches trademark law at the University of Minnesota’s law school, reviewed Becker’s applications and said she’s misinterpreting the law. Trademark is established by actually using the name, he said, not just filing the paperwork first.

“That’s not how this works,” he said. “That’s not how any of this works. You don’t get to steal someone’s brand out from under them by filing an application for registration — especially one that doesn’t have any use for it yet.”

So even though Edwards hasn’t filed the paperwork, he still retains rights to the name, McGeveran said. “First day of trademark class, I tell students: What creates trademark rights is using the name. Not registration. Registration’s a piece of paper.”