LYON, France -- When Trinity Rodman came into the locker room after the U.S. women's national team victory over Australia last week at the Paris Olympics, she was carrying a piece of paper that a fan thrust at her as she'd walked off the field. The paper had printed on it the names of the three starting American forwards -- Rodman, Sophia Smith and Mallory Swanson -- and then, in big, colorful letters, the words: "THE HOLY TRINITY."

Rodman was torn. While very much appreciative of the sentiment behind the sign, she remained optimistic (hopeful, even?) that a different nickname for the trio could be found. "I don't want it to be just, like, my name," she said. "So, we'll try something else."

That lack of an obvious (and catchy) moniker for the USWNT's front three is perhaps the only issue they've had over the past four games. As the U.S. prepares for its Olympic soccer semifinal here Tuesday against Germany, the Americans can take comfort in knowing that their primary scorers have been doing exactly that: scoring.

After Rodman's outrageous, extra-time game winner into the upper corner in the 1-0 quarterfinal victory against Japan, she and Swanson share the team's scoring lead with three goals apiece while Smith has added two goals of her own. Between them, they've scored eight of the team's 10 goals at the Paris Games.

"I feel like we're clicking really well, really fast," Smith said. "This is only like 70% of what we can do. The more games we get together, the more we're going to be playing off each other and just learning each other's tendencies. It's so much fun playing with them."

That level of comfort is clearly something new coach Emma Hayes has prioritized. Despite the compressed nature of the Olympic tournament, Hayes has been adamant about keeping her preferred lineup together -- even doing so in an all-but-dead-match against the Matildas in the group stage finale. While that decision is one that inspired some debate among observers who wonder about fatigue, the minutes the U.S. players are getting on the field -- especially among the front three -- have led to valuable understanding.

In the 4-1 group stage win over Germany, Rodman created the opening goal with a move on the edge of the penalty area that she then crossed perfectly to Smith, who finished first-time. It was a goal straight from the practice field, and it highlighted how quickly the U.S. forwards are taking in what Hayes -- who called the trio "dynamic as hell" -- wants from them.

"I think we're all really starting to come around to the way Emma has wanted us to play," Swanson said. "It's been really enjoyable just being able to learn different things and trying to apply them, especially since the group that we have is super special."

Swanson's appreciation for her part in this team's rise is understandable. She has been a part of the USWNT since 2016, when she was just 17, and she worked her way into a main role with the national team as she became a star in the NWSL. But three months before the Women's World Cup last year, Swanson tore her left patella tendon -- a devastating injury that required a full year of recovery.

Missing that much time was costly, both for Swanson's own confidence as well as her ability to mesh with Smith and Rodman, the other young attackers with whom she'd have to combine. During her time at these Olympics, she's found herself lingering on the basic premise that she is finally playing again without fear. "I think I'm just grateful," she said.

One thing that helped Swanson reintegrate so smoothly is her familiarity with Smith. While Smith is two years younger, she and Swanson both grew up playing for the same club near Denver, and they have been familiar with each other's games for years.

Swanson knows, then, the challenge that Smith has faced in playing a different role for the national team than the one she normally fills for her club team. With the Portland Thorns, Smith is often seen dropping back deeper into the field, playing the ball farther away from the goal.

With the USWNT, Hayes has been pushing her to get into the penalty area and look to take advantage of crosses, cutbacks and rebounds or unexpected bounces that fall to her there. It's something Smith is open to doing, but also a change that is requiring her to re-train her brain a bit.

"I think Emma's biggest goal for me is playing this [No. 9] position," Smith said. "I tend to kind of check into the pockets, get it and turn and go myself. It's obviously different here. I have players all around me that can do that, and I just need to find myself in the box to put away the chances that they're putting in there."

Staying more central is critical, too, because it opens space on the edges for Swanson as well as Rodman, who powered the U.S. into the semifinals with her wondrous sequence against Japan that began on the right sideline. That play -- where Rodman took down a ball from Crystal Dunn, dribbled toward the goal line before cutting sharply inside and blasting an inch-perfect shot into the upper corner at the far post -- was just the latest example of the individual brilliance that the USWNT has come to expect from Rodman.

At 22, she is already a mainstay of the U.S. attack and, even more to Hayes' liking, she is a two-way player with a significant motor, working back to help on defense as much as she surges forward. Despite being the third-youngest player on the Olympic roster, Rodman already has 44 USWNT caps and is the only American to appear in every USWNT game since the start of 2023. But while she was part of the team that crashed out of the Women's World Cup last summer in the round of 16, her impact there wasn't anything close to what it has been in France. For Rodman, much of that is due to Hayes' influence.

"The way that she coaches is she doesn't want to change anybody's style," Rodman said. "She wants everyone to be creative in their own ways and she lets that happen while also trying to put her structure and her principles sprinkled in there. But allowing us to play free I think has been extremely successful."

That much, certainly, is sure. And as the USWNT recasts itself under Hayes, it's impossible to overstate how important the three players leading the line are to the new personality of this group. Lindsey Horan, the veteran midfielder and captain of the team, drew a clear line between what Rodman, Smith and Swanson are doing and the emergence of a new feeling around the team as a whole. Even if they don't have a catchy nickname just yet.

"We keep talking about this new identity, this new style, this new sense of confidence," Horan said. "I think you see it in our front three. I think you see it in our attack ... I think that's the key for us right now."