Is Cleveland big enough for two sports teams named the Guardians? A roller derby team that has used the name since 2013 says no.

The roller derby Cleveland Guardians sued the city’s Major League Baseball team in federal court on Wednesday in an effort to block the baseball team from changing its name to the Cleveland Guardians, contending that the change infringes on the roller derby team’s trademark rights.

The baseball team announced in July that it was changing its name from the Indians to the Guardians after years of pressure to veer away from a team name that many considered racist toward Indigenous people.

The coed roller derby team, which operates in the Cleveland suburb of Parma, Ohio, has been called the Guardians since 2013 and formally registered the name “Cleveland Guardians” with the Ohio secretary of state in 2017, according to its lawsuit filed on Wednesday in U.S. District Court for the Northern District of Ohio.

In the lawsuit, Guardians Roller Derby v. Cleveland Guardians Baseball Company L.L.C., the roller derby team claims that the M.L.B. team knew the Guardians existed months before the name change was announced.

“A Major League club cannot simply take a smaller team’s name and use it for itself,” the lawsuit says. “Economic might, however, does not make legal right. There cannot be two ‘Cleveland Guardians’ teams in Cleveland, and, to be blunt, Plaintiff was here first.”

The lawsuit also claims the M.L.B. team filed its trademark application in Mauritius, a small East African island nation, and that in doing so the baseball team was “effectively hiding the application unless one knew where to look.”

The baseball team said in a statement on Wednesday that it was in the right.

“We have been and continue to be confident in our position to become the Guardians,” the baseball team said. “We believe there is no conflict between the parties and their ability to operate in their respective business areas.”

Two months after the baseball team filed its trademark application, it contacted the roller derby team to inform it of the name change, according to the lawsuit. As the two teams corresponded, Gary Sweatt, the owner of Guardians Roller Derby, offered to sell the rights to his team’s names, including the website, and invited the M.L.B. team to make an offer.

In June, the M.L.B. team offered to pay “a nominal amount,” the lawsuit said. Mr. Sweatt rejected the offer and countered with another proposal, which the baseball team did not address, according to the lawsuit. In July, the baseball team announced its name change with a theatrical video posted online that was narrated by Tom Hanks.

When the baseball team announced the name change, the team said it would finish the 2021 season as the Indians and would “look to launch as the Cleveland Guardians at the conclusion of the season.”

In a statement on Wednesday, Mr. Sweatt, the owner of Guardians Roller Derby, said the team believes it is “in the right.”

“Just like our athletes do on the track, we will put everything into this effort at the courthouse,” he said.

The roller derby team is a nonprofit organization, and any profits made from Cleveland Guardians merchandise are used to provide “funding for training its skaters and for hosting community events,” the lawsuit said.

As of Wednesday night, the ClevelandGuardians.com website still displayed the roller derby team’s content, as did Facebook.com/clevelandguardians. The baseball team still uses Indians.com as its website and the Twitter handle @indians.

In the lawsuit, the roller derby team said it was “inconceivable that an organization worth more than $1B and estimated to have annual revenues of $290M+ would not have at least performed a Google search for ‘Cleveland Guardians’ before settling on the name.”

In a statement, Christopher Pardo, the lead lawyer for the roller derby team, said the baseball team “knowingly and willfully eviscerated the rights of the original owner of that name — the Cleveland Guardians.”

“Major League Baseball would never let someone name their lacrosse team the ‘Chicago Cubs’ if the team was in Chicago, or their soccer team the ‘New York Yankees’ if that team was in New York — nor should they,” Mr. Pardo said. “The same laws that protect Major League Baseball from the brand confusion that would occur in those examples also operate in reverse to prevent what the Indians are trying to do here.”