Pilots will play a pivotal role in that process, a Boeing spokesman told Reuters.

"Pilots' confidence in the aircraft will lead passengers and crew to have greater confidence in the aircraft," said Gordon Johndroe, vice president for communications at Boeing.

A person familiar with Boeing's public trust campaign said they did not believe the company was contemplating renaming the MAX, noting that aircraft renaming is a large undertaking that goes far beyond just a new paint job.

For now Boeing remains focused on submitting a software update and finalising pilot training for regulatory approval. Regulators worldwide are preparing to review Boeing's proposals.

In an early-morning post on Twitter, Trump, who owned the Trump Shuttle airline from 1989 to 1992 and is an aviation enthusiast, weighed in with his own advice.

"What do I know about branding, maybe nothing (but I did become President!), but if I were Boeing, I would FIX the Boeing 737 MAX, add some additional great features, & REBRAND the plane with a new name. No product has suffered like this one. But again, what the hell do I know?" Trump tweeted.

The plane's grounding has also threatened the U.S. summer travel season, with some airlines removing the 737 from their schedules through August.

The 737 MAX is Chicago-based Boeing's fastest-selling jet and its main source of profits and cash, having won some 5,000 orders or around seven years of production for the aircraft.

Chief Executive Dennis Muilenburg has apologised on behalf of Boeing for lives lost in two recent accidents and promised it would address the risk that flight software meant to prevent the plane stalling could be activated by wrong data.

BRANDING STRATEGY 'PREMATURE'

Boeing has also held dozens of briefings and simulator sessions for airline executives and pilots as well as worldwide meetings with airline branding and communications staff, but Trump's tweet marks the first time the brand underpinning Boeing profits in coming years has been thrown into question at such a high level.

Brand Finance, a UK-based consultancy that tracks the value of global brands, rejected the idea that Boeing should abandon the MAX brand but said its corporate reputation was in the firing line.

"This has without a doubt damaged Boeing's reputation and we foresee a dent to the (Boeing) brand's value at over $12 billion," Chief Executive David Haigh said by email when asked about Trump's comments.

"This is a temporary blip in the long run for Boeing," he said, adding Toyota and others had recovered from similar high-profile crises without a drastic rebranding exercise.

Brand Finance had previously estimated the damage to the value of Boeing's reputation at $7.5 billion immediately after the March 10 crash of an Ethiopian Airlines jetliner, the second fatal accident involving the 737 MAX in five months.

Benjamin Hordell, founder of marketing and advertising firm DXagency, said just renaming the plane alone was not enough. Boeing should use this as an opportunity to rebrand the company by being more transparent about the steps it takes. "People will look at it and know that it's the Boeing 737 MAX under a different name," he said.

"To rebrand without making sure the product is safe, and undergoing another crash with the same airplane under a new name and image could destroy Boeing," said Paul Caiozzo, founder and Chief Creative Officer of brand design agency Interesting Development. "It is premature to begin to talk about rebranding a plane that has not yet been fixed."

Boeing has the world's most valuable aerospace brand, with the value of its overall corporate image rising 61 percent to $32 billion in 2018, according to Brand Finance.

(Reporting by Susan Heavey in Washington, Tracy Rucinski in Chicago and Tim Hepher in Paris; Additional reporting by Helen Coster and Sheila Dang in New York and Allison Lampert in Montreal; Editing by Jeffrey Benkoe, Toby Chopra and Richard Chang)

By Susan Heavey and Tracy Rucinski