Snyder, who has previously stated he would not change the name, softened his stance a day after FedEx Corp, which owns the naming rights to the team's Landover, Maryland, stadium, called for the NFL club to be rebranded.
The NFL team said in a statement that in light of recent events around the country and feedback from the community that it will undergo a thorough review of the name.
"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.
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A story on the NFL website on Friday reported that a group of 87 investment firms and shareholders had signed three separate letters to FedEx, Nike Inc and PepsiCo Inc to terminate relationships with the team unless it changed its name.
PepsiCo followed FedEx's lead in speaking up on Friday. It issued a statement that it welcomed Snyder's call for a review of the team's name.
"We have been in conversations with the NFL and Washington management for a few weeks about this issue. We believe it is time for a change," a PepsiCo representative said on Friday. "We are pleased to see the steps the team announced today, and we look forward to continued partnership.”
Critics have ramped up pressure on the team to change its name, which is widely seen as a racial slur against Native Americans, after the death of George Floyd, a Black man who died in police custody in Minneapolis. Floyd's death on May 25 has triggered worldwide protests against racism and police brutality.
NFL Commissioner Roger Goodell said in a statement on the league's website that he was supportive of Snyder's move to look at a possible name change.
"In the last few weeks we have had ongoing discussions with Dan and we are supportive of this important step," Goodell said.
Symbols, statues and awards connected to the United States' racist past have been under attack in recent weeks.
Last month a memorial to late Washington Redskins' founding owner, George Preston Marshall, who fought against the racial integration of the NFL, was removed from RFK Stadium, the team's former home.
Major League Baseball's Minnesota Twins also removed a statue of their late former owner, Calvin Griffith, from outside Target Field in Minneapolis because of racist comments he made decades ago.
NASCAR banned the Confederate flag, which many Americans see as a symbol of oppression and slavery, from all race tracks and events while the Professional Golfers' Association of America on Thursday renamed the Horton Smith award which was named for a former PGA president who supported a "Caucasian-only" membership clause.
The team that became the Washington Redskins was founded in 1932 as the Boston Braves. They changed their name to the Redskins the following year and moved to Washington, D.C., in 1937.
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