The switch, proposed by Senator Chuck Schumer, Democrat of NY, would erase the name of Senator Richard B. Russell of Georgia, a segregationist Democrat who led southern opposition to the civil rights movement, from the oldest of the US Senate office buildings.
Saturday's motorcade was only the beginning of several opportunities for people to pay their respects to Senator McCain.
President Donald Trump was not expected to attend any of the services.
McCain's widow Cindy is among potential candidates to take the late senator's seat until the special election in 2020, the media reported. Privately, he has groused about such slights as his belief that McCain did not appreciate his endorsement in the senator's 2016 re-election bid. "As Chairman and longtime member of the Armed Services Committee, Senator McCain consistently worked to ensure that Israel had the critical resources to defend herself".
PolitiFact went to the White House to document the flag's status. John McCain, are back at full-staff.
Russell's legislative accomplishments were many: He backed the New Deal in the 1930s; authored the National School Lunch Act, which provided meals for low-income students while also subsidizing the nation's farmers; and ardently supported the military.
McCain and Trump were not exactly best buddies during the President's first 20 months in office.
Prior to the statement, Trump had only tweeted his "deepest sympathies and respect" to the McCain family.
McCain, who's remembered by most as an American hero, will be laid to rest at the U.S. Naval Academy's cemetery in Annapolis, Maryland on Sunday.
In death, McCain himself had more to say.
Sen. John McCain, R-Ariz., walked through the Senate subway in July 2017.
Republican Sen. James Inhofe of Oklahoma allowed that McCain "was partially to blame" for the rift with Trump, saying, "He was very outspoken that he disagreed with the president in certain areas and wasn't too courteous about it". "He was a true giant in the Senate, and he will be deeply missed".
Trump and McCain were at bitter odds until the end. Trump questioned the decorated Navy pilot's Vietnam heroism and chafed at McCain's vote to kill the president's "Obamacare" repeal.
"I have often observed that I am the luckiest person on earth".
Putting McCain's name there instead honors a war hero and Republican senator known for reaching across the aisle.
Trump feuded with McCain and has refused to talk about him since his death on Saturday.