This black & white picture below is of a company model that Boeing said might be their 777. At the time, in 1977, it was designated 7X7. It was to be a 200-seat plane with three small engines, twin-aisles and with longer range for which American Airlines was to be the launch customer.
However at the time, United Airlines wanted a smaller, single-aisle, twin-engined plane for shorter routes.
In 1978, Boeing considered making both. Boeing gave the designation 777 to their 3-engined design. They gave the designation 767 to their twin-engined design.
But they then realized that larger versions of the 7N7 would be almost overlapping with the 7X7.
However, Eastern Airlines and British Airways soon both expressed interest in a smaller, single-aisle twin, eliminating the quandry of which way to go.
Boeing then made the obvious decision. They decided to make the larger, twin-aisled plane to satisfy American Airlines, but only with two, albeit larger, engines. They then designated it 767.
They then satisfied Eastern and British Airways and United by making the 7N7 and launching it as the 757. Below is as it would have appeared in Eastern Colors. The T-tail was dropped.
The 3-engined 7X7 was shelved until 1990. Somewhere along the way it lost an engine. Pity.