TOKYO—For most athletes, getting ready for the Olympics involves training camps, trial competitions and mental preparation. For Russians, it also includes horse-trading over bears and music. 

Caught in a doping scandal, Russia has been stripped of its key identifying markers like a flag or a national anthem. Russia, in fact, isn’t officially competing in Tokyo as a country. Its athletes are competing as ROC, for the Russian Olympic Committee.

In December, the Court of Arbitration for Sport in Switzerland banned Russia from international sports until the end of 2022 after the World Anti-Doping Agency found it guilty of running a state-sponsored doping program. Clean Russian athletes were allowed to participate in Tokyo, under strict guidelines. The International Olympic Committee said that any deviation from the guidelines could lead to new court cases. 

So ahead of the Tokyo Games, Russian officials and the IOC had to hammer out details including the kind of music to play for their winners instead of the national anthem, what the uniforms would look like and where Russian flags can or can’t be positioned (venues are a no-go but hotels can fly the Russian banner). 

Tokyo is the third Olympics where Russians will compete with their country either partially or fully banned. Around 330 athletes will represent the ROC in Tokyo. 

“It’s insulting…but as they say, if the flag is not allowed, we ourselves will be the flag,” Alena Tiron, the captain of the Russian rugby team, told state news agency RIA Novosti. “We know which country we stand for.” 

Flag bearers Sofya Velikaya and Maxim Mikhaylov of Team ROC lead their team out.

Flag bearers Sofya Velikaya and Maxim Mikhaylov of Team ROC lead their team out.

Photo: Jamie Squire/Getty Images

Before the Games, the artistic swimming team sent the IOC a sketch of their swimwear for approval. The IOC sent it back because it featured the image of a bear, one of Russia’s symbols. The Russian costume designer had to quickly draw up new versions.

“It’s a very strange decision,” Olga Brusnikina, first vice-president of Russia’s Synchronized Swimming Federation, told RIA. “Bears, after all, live not only in Russia, but in Canada and America, too.”

The Kremlin saw a silver lining.

“Let’s look at it from the other side: The IOC has officially recognized the bear as a symbol of Russia,” Dmitry Peskov, the spokesman for President Vladimir Putin, told reporters. “This is not a bad thing.”

Another issue facing the artistic swimming team was their choice of music for their routine, “With Russia from Love” by local rave band Little Big. The IOC didn’t ban the song but decreed that the word Russia will have to be cut. 

This wasn’t Russia’s only musical problem.

Unable to play their national anthem, the Russian Olympic Committee proposed “Katyusha,” a Soviet folk-based song usually identified with the fight against Nazi Germany in World War II. The IOC rejected it and a compromise was found: a fragment of Piano Concerto No. 1 by composer Pyotr Ilyich Tchaikovsky. The piece will also be used at the 2022 Winter Olympics in Beijing.

Russians are also banned from sporting their country’s tricolour flag on their uniforms. But the kit, including jackets and shirts, still features blue, red and white in the order they appear on the flag, eliciting criticism from some international commentators and officials.

“We’re disappointed that Russian athletes can wear the colors of the Russian flag on their uniform,” WADA’s president Witold Banka said in an interview. “We thought that there should have been a neutral status for Russia.”

Stanislav Pozdnyakov, ROC’s president and a five-time Olympic medalist in fencing, said that the Russian team would have “all the elements of its identity.” Russia’s sports minister Oleg Matytsin said that the uniform is “beyond doubt is associated with our country.” 

“I am sure that all spectators of the Games will understand that these are representatives of Russia,” Mr. Matytsin said. 

PutinTeam, a movement supporting Russian President Vladimir Putin started by NHL player Alexander Ovechkin in 2017, has listed the social media accounts of all Russian athletes competing in Tokyo on its website, urging people to follow and support them. 

Soviet hockey legends Vitali Prokhorov, Alexei Kasatonov and Viacheslav Fetisov posted a video on the PutinTeam website to support the team “in a difficult and unfair situation, when representatives of Russia perform at the main competition of their lives without the flag and anthem of their country, without the support of fans, with empty stands.”

On Instagram, meanwhile, influencers have posted hundreds of pictures of support for the Russian team using the hashtag #wewillROCyou. The hashtag received an official seal of approval from Foreign Minister Sergey Lavrov. “This abbreviation obliges us to additionally try to defeat everyone,” he said.

Silver medalist Anastasiia Galashina of Team ROC poses during the medal ceremony for the 10m Air Rifle Women’s event.

Silver medalist Anastasiia Galashina of Team ROC poses during the medal ceremony for the 10m Air Rifle Women’s event.

Photo: Kevin C. Cox/Getty Images

The ROC has instructed its athletes to say that they still represent Russia despite the flag ban and that they would have liked to hear the national anthem “because this is always a very emotional moment,” according to reports in Russian media confirmed by the Kremlin. The ROC didn’t respond to a request for comment. 

“It so happened that we will have to perform without the Russian tricolor, without the Russian anthem that we could sing loudly and in unison,” artistic swimmer Svetlana Romashina, whose bear uniform had to be amended, told Mr. Putin at a ceremony at the Kremlin last month. 

“But the most important thing is that Russian fans and fans from all over the world know which country we represent,” Romashina said. “And most importantly, loyalty and love for our country is here, within us, and no one will ever take this away from us.”

Write to Georgi Kantchev at georgi.kantchev@wsj.com