Well yes it did, although Boeing used the term to refer to the former Rockwell operations rather than the company as a whole. After the McDonnell Douglas acquisition that branding fell into disuse.
Of course it might have been one of our august SPF members who wrote of the merger, "it was a McDonnell-Douglas takeover of Boeing using Boeing's money" in recognition of the fact that McDonnell Douglas figures were now major shareholders in Boeing, such as McDonnell the Younger and Harry Rockzero. Luckily they were put to pasture before they did to Boeing what they had done to McDonnell Douglas.