McLean-based Science Applications International Corp.’s decision to split itself in two prompted an immediate question.

What to call the two companies?

To get an answer, SAIC turned to Interbrand, a brand consulting firm that counts among its clients companies from Bing to Dunkin’ Donuts to Porsche, among many others.

Interbrand rounded up 3,400 possibilities and then went to work checking which ones were already in use in dozens of countries, winnowing the list to 64 candidates.

Ultimately, SAIC decided to continue calling one company SAIC and dubbed the other Leidos, a name meant to call to mind a kaleidoscope and illustrate SAIC’s ability to bring different perspectives and ideas to problem-solving in the engineering, health and national security arenas.

The logo for Leidos.

The branding process represents just one step along the road to a significant split of the sprawling government contractor. SAIC announced last year that it would divide into two pieces: a roughly $4 billion publicly traded company focused on government services — which will retain the SAIC name — and a roughly $7 billion publicly traded company specializing in technology for the national security, health and engineering sectors.

Interbrand executives said they made multiple trips to SAIC to interview company officials representing the SAIC and Leidos pieces.

Christina Stanfield, senior director of strategy at Interbrand, said the company conducted about 50 interviews, asking company employees about the capabilities, values and aspirations of the company.

SAIC employees, whether working on national security, health or engineering, generally approached their work similarly, Stanfield said, leading Interbrand to consider metaphors related to cross-pollination among sectors and problem-solving through new perspectives.

‘Metaphor territories’

The agency weighed close to a dozen metaphors that might communicate how the firm worked, including the idea of a great race, such as the space race or the Olympics.

After settling on two or three “metaphor territories,” Interbrand then came up with name candidates, including actual words, combinations of words and made-up words.

“The name for us had to have a meaning behind it ... that articulates what our people do, perhaps not in an obvious way, but in a way that is not too abstract,” K. Stuart Shea, chief operating officer of the still-whole SAIC who will be president and COO of Leidos, said in an e-mail.

Still, of 3,400 potential names, just several dozen were available. One well-liked choice already had a trademark filed, while another sounded too much like a prominent company.

Once the names were further narrowed, SAIC commissioned deeper investigations to ensure potential names were legally available. Each of these international searches — which covered the 40 countries in which SAIC operates — cost about $100,000, said Melissa Koskovich, an SAIC spokeswoman; the company paid for about a half dozen.

SAIC said it paid Interbrand about $1 million for its work, which spanned 18 months (including a five-month naming period).

Leidos — clipped from the word kaleidoscope — was available, and both SAIC and Interbrand officials liked the metaphor, Stanfield said.

“The unique kind of capability that we saw [in SAIC] came from combining things in unexpected ways,” she said. “You get this transformation into brilliant new images.”

Interbrand came up with 10 logo options for Leidos, but the companies eventually settled on one using a triangle — the symbol for change — being pulled and layered.

The logo uses purple, a rare color in the defense contracting world.

Despite the months of effort, the new name hasn’t been an unqualified success. Shea said company leadership has received feedback for and against Leidos.

The company got a vote of support from one former employee. J. Robert Beyster, SAIC’s retired founder who served for more than three decades as chief executive, wrote on his blog that he approves of the new name.

“While I personally do not agree with splitting up the company, I can live with this new name,” he wrote. “It’s not bad.”