House Republicans have settled on a name for their tax overhaul bill: "the Tax Cuts and Jobs Act," multiple sources confirmed to ABC News.

President Donald Trump had told senior congressional leaders that he wants to name the bill “the Cut Cut Cut Act,” two senior administration officials told ABC News. The bill will be unveiled today.

There was still dispute over the name as of Wednesday, according to a senior congressional aide and a senior White House official.

The sources said the Ways and Means Committee would have the final say.

Still, behind closed doors, there was back-and-forth between House Speaker Paul Ryan and House Ways and Means Committee Chairman Kevin Brady about the name of the bill, including multiple phone calls in the past week.

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Ryan's office initially asked the White House for input because of the president's knack for branding, according to a senior Hill aide.

Trump has been insistent that the bill be called "the Cut Cut Cut Act," according to the administration officials.

Ryan and Brady have pushed back on the name of the bill. Trump, however, has held firm.

Internal White House polling showed that Americans respond more favorably to language that highlights tax cuts over tax reform, according to a senior White House official.

“At the end of the day, this will be known as the Trump tax cuts,” the senior Hill aide said.

Brady’s office declined to comment.

After the White House did not respond to ABC News' request for comment, press secretary Sarah Sanders joked about the potential name of the bill at Wednesday's press briefing.

"If it's called 'cut cut cut' and it includes massive tax cuts like this president is proposing, I think we would be perfectly fine with that name," Sanders said.

AshLee Strong, Ryan's national press secretary, called the branding of the bill a “total nonissue.”

Asked whether it’s unusual for the White House to take a role in the branding of legislation, she explained that “with a Republican president, it seems you’d want to have involvement.”

“The fact that he wanted to name the bill, that is hilarious and perfectly illustrates how — in things both large and small — the Hill can’t quite figure out Trump,” said a person with direct knowledge of the dispute.

Congress is set to reveal its much anticipated tax overhaul plan on Thursday, even though many details are still being ironed out, such as the threshold for curbing state and local tax deductions, limits on tax-exempt contributions to retirement plans like 401(k)s, child tax credits and property tax deductions.

ABC News’ Jonathan Karl and John Parkinson contributed to this report.