Night City is on the west coast of North America. The world in cyberpunk is heavily controlled by global influences, of which the Japanese Arasaka is arguably the largest.
You've never seen any cyberpunk movies or books? They're all like that. Cyberpunk was made during a time where Japan was at the forefront of technology, every device you bought came from them. So people could easily imagine a future where Japan becomes a major world power and Japanese a kind of new lingua franca