“I keep them in dust bags because I feel like my daughter might grow up and want to borrow them,” Osaka said. Her daughter, who is 3, is “so opinionated,” she said. “She loves a dress.” Osaka also has an apartment in Dumbo, where at the moment there is a rack of dresses and heels for her practice looks, and in the mornings her daughter helps her choose what to wear.

When Nike told her its theme for the U.S. Open, Osaka said, “I kind of sat with that for a while because, honestly, basketball doesn’t really mean much to me. But eventually I started thinking about players that have impacted the sport, and that, style-wise, have changed the game.” That led her to Iverson, the former Philadelphia 76er who brought hip-hop style to the league.

“He’s shifted the way N.B.A. players dress, and the whole conversation around clothes in sports, and expressing yourself through style,” Osaka said in a news conference before the Open. (She was wearing an Iverson T-shirt at the time, in case anyone didn’t get it.) Now she is trying to do the same.

After she won her first match at the U.S. Open, when she was fielding questions from the press about the surprisingly close match, she deftly used fashion to change the focus. “I just get really nervous during the first round of this tournament, because I want to do well,” she said. “And I want to show you guys some more outfits.”

Soon she may not be the only one. At Wimbledon, Nair said: “I was watching Aryna Sabalenka watching Osaka come out, and there was clearly a kind of upmanship going on. Like, ‘Yeah, I could do something like that.’ And I thought: ‘This is what is coming. It’s going to be a red carpet on the tennis court. Soon, people are going to be lining up and saying, ‘What are you wearing?’ before they go on.”

Callie Holtermann contributed reporting.