BROOKLYN, N.Y.—The conversation on the street, in stores and in restaurants in Brooklyn’s “Little Odessa” neighborhood is in Russian. Storefronts and cars are festooned with blue-and-yellow Ukrainian flags.

In one of the largest Russian and Ukrainian communities in America, most people oppose Russian President Vladimir Putin and Russia’s invasion of Ukraine, residents and community leaders say, and many visibly show their support for Ukraine.

Bobby Rakhman, co-owner of a Brighton Beach grocery specializing in foods from the former Soviet Union, said some of the clientele—which is mainly Russian-speaking immigrants and people with roots in post-Soviet countries—had expressed discomfort with the business’s name, Taste of Russia, since the Ukraine war began.

Sometime after the Russian invasion of Ukraine, Bobby Rakhman changed the name of the Brighton Beach market he co-owns, from Taste of Russia to International Food.

So in March, Mr. Rakhman, a 51-year-old Odessa native, changed the name to International Food, discarding the old moniker which had been in place for more than three decades. The difference, he said, has been appreciated by shoppers.

“ ‘International Food’ is basically a neutral name,” he said.

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The area of south Brooklyn centered in the neighborhood of Brighton Beach earned the nickname “Little Odessa” after thousands of Soviet Jews arrived there from Ukraine in the 1970s.

Living there are immigrants from Kyiv, Moscow, and other cities in the former Soviet Union. Stores sell Eastern European goods, and many signs are in Russian. About 600,000 Russian Americans live in New York City, according to the advertising firm Ameredia.

A popular store in Brighton Beach serves mainly of Russian-speaking immigrants and people whose families come from post-Soviet countries.

The co-owner of International Food said some customers had conveyed discomfort with the store’s old name, Taste of Russia.

Samantha Shokin, 32, whose parents came to New York from Ukraine and Lithuania and met in Brooklyn, handed out fliers for a pro-Ukraine march staged in Brighton Beach. She said the March 19 protest organized by RUSA LGBTQ+, a gay-rights advocacy group for Russian-speaking Americans, drew about 200 people. The march wound along Brighton Beach’s seaside boardwalk and past homes with Ukrainian flags in their windows, Ms. Shokin said.

“The vast majority of people are on the side of Ukraine,” she said. “People want to distance themselves from Russian and even Russian-speaking culture.…All of this has become a million times more complicated because of the war.”

Samantha Shokin, whose parents came to New York from Ukraine and Lithuania, drummed up support for a pro-Ukraine march.

In one of the area’s most visible confrontations over the war, a resident of Gravesend, a neighborhood adjacent to Brighton Beach, was assaulted March 15 while unfurling a flag supporting Ukraine’s pro-Russian separatists in his front yard, according to the New York City Police Department. A suspect was arrested that day and charged with a hate crime, an NYPD spokesman said.

Dmytro Druzenko, a worker at Galaxy Tire Shop in Brighton Beach, said days after the war began, employees at his business hung a sign with a picture of Mr. Putin and a Russian-language insult on their busy, corner storefront.

Days later, the sign was gone. Workers put up another sign. Within days, it was gone, too, snatched away during the night.

Mr. Druzenko said he hadn’t expected to be bothered by Putin supporters in a neighborhood where most residents are united against the war. He said Galaxy employees had since rehung their anti-Putin posters, this time placing them high on the side of the building so they can’t be reached by vandals.

On Tuesday, Russian-speaking customers in cars bearing blue-and-yellow Ukrainian flags pulled up to be serviced.  “They understand,” Mr. Druzenko said.

A section of Brighton Beach—from the beach.

—Elisa Cho contributed to this article

Write to Ben Chapman at Ben.Chapman@wsj.com