Rivera told the Washington Post that he is hopeful the "Redskins" name could be changed in time for the 2020 season.
"If we get it done it time for the season, it would be awesome," Rivera told the newspaper Saturday. "We came up with a couple of names -- two of them I really like."
The former Carolina Panthers head coach, who was hired by the Redskins in January, said it's important that a new team name respects Native American traditions and culture, while also paying tribute to the military.
Rivera -- who is of Mexican and Puerto Rican descent and is the only current Hispanic head coach in the NFL -- is the son of an Army officer.
"We want to do this in a positive way," Rivera said.
The Redskins are expected to change their nickname after the franchise announced Friday that it will "undergo a thorough review" of the team's name. The name has come under increased scrutiny amid social unrest around the country after the killing of George Floyd in Minnesota at the end of May.
"This process allows the team to take into account not only the proud tradition and history of the franchise but also input from our alumni, the organization, sponsors, the National Football League and the local community it is proud to represent on and off the field," Snyder said in a statement Friday.
NFL commissioner Roger Goodell said in a statement Friday that the league has had "ongoing discussions" with Snyder and is "supportive of this important step."
On Thursday, FedEx -- which holds the naming rights to the Redskins' stadium -- asked the team to change its name. Frederick Smith, the chairman, CEO and president of FedEx Corp., holds a minority stake in the team.
Also Thursday, Nike appeared to remove all Redskins gear from its online shop, and PepsiCo was reportedly under pressure to sever its sponsorship with the franchise.