Ted S. Warren, Associated Press
FILE - This Dec. 7, 2015, file photo shows the second Boeing 737 MAX airplane being built on the assembly line in Renton, Wash. The president of the pilots' union at American Airlines says Boeing made mistakes in its design of the 737 Max and not telling pilots about new flight-control software on the plane.

SALT LAKE CITY — Travelers may or may not know or care if they're boarding a Boeing 737 Max, the aircraft that made headlines after two fatal crashes occurred within six months, killing 346 people.

But for those who worry, Greg Smith, the company’s chief financial officer, recently suggested a way to relieve their concern and restore their trust: drop the "Max" branding.

“We’re committed to doing what we need to do to restore it. If that means changing the brand to restore it, then we’ll address that. If it doesn’t, we’ll address whatever is a high priority,” Smith told Bloomberg at the Paris Air Show.

The data is mixed on whether the public fears flying on the 737 Max. A recent study by the Atmosphere Research Group showed that 14 percent of Americans would be willing to get back on a 737 Max, while 65 percent aren’t sure if they would, even after a year of returned service, the Los Angeles Times reported.

However, 65 percent of participants in another survey by UBS, a financial services firm, said they don’t look at what kind of plane they are flying on, according to Market Watch.

But, as Kevin Michaels of the AeroDynamic Advisory pointed out to CNBC, "Usually the public doesn't care what aircraft they're on. Now they do."

The bad press in the wake of the crashes has Boeing trying to regain customers’ trust. In May, the The New York Times reported that Boeing knew of a mechanical error that contributed to the fatal crashes and failed to report it to the Federal Aviation Administration. The problem involved a warning light that did not work unless the aircraft included an indicator that was not automatically included in the model.

According to the Seattle Times, Boeing did not plan on fixing the issue until 2020.

While top competitor Airbus released a new plane at the Air Show, Boeing executives were apologizing for the crashes and once again making promises to increase focus on safety and transparency, according to The Associated Press.

" We should design aircraft for them (pilots) to fly that do not have inadvertent traps set for them. "
Chesley “Sully” Sullenberger

Boeing still has not announced when the 737 Max planes will return to the skies. The Wall Street Journal reported Wednesday that further delays are being caused by fears that an emergency crank that would help move the plane’s nose is too difficult for the average pilot to move. However, FAA regulators told CNBC that the issue of pilot strength was not causing delays.

Earlier in the week Reuters broke the news that the company planned to reduce the number of physical tests on the 777 X, a new plane currently in development. The plan is to use digital simulations rather than costly time spent in the air and stress tests that include bending the wings of the plane.

In the latest round of critiques of Boeing, Daniel Carey, a captain with American Airlines and head of its pilots union, stated concerns about the training of pilots Wednesday at a House Subcomittee on Aviation hearing on the status of the Boeing 737 Max. At the hearing, Carey asked if “the FAA is sufficiently independent of the manufacturers as to provide legitimately rigorous audit of manufacturing, design and engineering?”

Chesley “Sully” Sullenberger, a retired pilot famous for safely landing a plane on the Hudson River in 2009, also testified at the congressional hearing. He said Boeing added the Maneuvering Characteristics Augmentation System but did not tell pilots until after the first crash.

“We should design aircraft for them (pilots) to fly that do not have inadvertent traps set for them,” said Sullenberger.

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One bit of good press for Boeing came Tuesday when the International Airlines Group announced it planned to place an order for the 737 MAX planes. Aerospace analyst Richard Aboulafia told CNN, "This is a very positive development for both sides. Boeing got a great endorsement from a respected airline group and IAG gets a heavily discounted jet.”

Before fulfilling those orders, however, Boeing has to prove to FAA regulators and convince the traveling public, that the 737 MAX is safe. Sara Nelson, president of the Flight Attendants Union told CNBC, "The process for implementing the fix and FAA certification must be transparent and conservative in order to restore confidence. We do very much want Boeing and the FAA to get this right so that we can advise crews and passengers that we are safe to fly. We're not there yet."