WASHINGTON—President Trump revealed plans to rebrand the North American Free Trade Agreement as the “USMC” pact—for the U.S., Mexico and Canada—telling Republican donors at a private fundraiser Wednesday that he will drop the “C” if Canada doesn’t agree to changes he is seeking, according to people familiar with the matter.

Mr. Trump groused about Canada during a private meeting with about a dozen supporters, complaining that officials from the U.S.’s northern neighbor describe themselves as good friends to America while imposing tariffs of more than 200% on some American dairy exports, these people said.

The president was described as jovial during the event—“He was in fine form,” one Republican said—but his exasperation with Canada found a receptive audience in Dan Stamper, president of Detroit International Bridge Co., who was among about a dozen corporate executives, Republican officials and other donors who met privately with Mr. Trump for a half-hour.

Related Video After the U.S. and Mexico announced a trade deal, Canada and the U.S. have resumed efforts to come to an agreement. WSJ's Shelby Holliday takes a look at some sticking points. Photo: Getty Images

The smaller meeting, designed to give donors more access to the president, cost $100,000 per seat. It was followed by a dinner of about 175 people that cost $35,000 a couple, according to a copy of the invitation.

The event raised $3 million for Trump Victory, a joint fundraising committee for the president’s campaign and the Republican National Committee, a Republican official said.

A spokeswoman for the RNC, which organized the event, declined to comment.

Speaking with the president, Mr. Stamper repeated many of the points in a TV ad his company aired this summer during the “Fox & Friends” morning program on Fox News, which is among Mr. Trump’s favorites. The spot implored the president to revoke permits issued by the Obama administration for construction of a publicly owned bridge between Detroit and Windsor, Ontario.

Mr. Stamper, who didn’t immediately respond to a request for comment, runs the company that owns the 87-year-old Ambassador Bridge that spans the Detroit River and charges tolls.

Officials from the Michigan Department of Transportation have disputed several assertions in the private company’s commercial and described it as misleading, according to the Detroit News.

The small group also included Dr. Rim Al-Bezem, a cardiologist whom the president credits with helping alert him to a potential massacre in Idlib, the northwestern province in Syria that has become the last refuge for millions of people and some 70,000 opposition fighters considered to be terrorists by the Assad regime, said people familiar with the matter.

The president referred to Dr. Al-Bezem without naming her in an interview with the Daily Caller this month, saying he met a woman in Indiana who warned him about the potential atrocity, and that he was thinking about her warning when he posted a message on Twitter saying it would be a “grave humanitarian mistake” for Syria, Russia and Iran if the attacks were carried out, said the people familiar with the matter.

Dr. Al-Bezem, whose identity hasn’t been previously reported, told Mr. Trump on Wednesday that his tweet saved tens of thousands of lives, an analysis the president agreed with, one person said. Dr. Al-Bezem, who didn’t immediately respond to a request for comment, also urged the president to send another tweet warning Syrian President Bashar al-Assad against using any conventional weapons in Idlib.

At the dinner, Mr. Trump listed dozens of economic statistics, including recent gains in the stock market and drops in the unemployment rate, said people familiar with the matter. Mr. Trump was joined at the dinner by Rep. Kevin Cramer, the Republican Senate nominee in North Dakota, and Sen. Mike Rounds (R., S.D.).

The president ticked through a list of employment rates for women, African-Americans and Asians, say they “should be voting for me.” Mr. Trump added that he would be amazed, given these statistics, if any Republican who supports him would lose, one person said.

“How can we lose?” he said.

—Julie Bykowicz contributed to this article.

Write to Michael C. Bender at Mike.Bender@wsj.com