The story
Brand name; according to Segway Inc., chosen for similarity to segue on notion of “a smooth transition from one place to another”, with probable influence of way.
Etymology from Wiktionary, CC BY-SA 4.0.
segway
Today it means: A motorised vehicle for one person, ridden while standing, and having two wheels on one axle that balances itself using gyroscopes and tilt sensors. Full definition →