What is the name for the seemingly fixed point around which the Northern night sky appears to pivot?

North celestial pole.

The north celestial pole is the specific location in the sky that serves as the stationary center for all apparent stellar motion in the Northern Hemisphere. This point is determined conceptually by extending the Earth's axis of rotation straight outward into the vastness of space until it intersects the celestial sphere. Because the Earth's axis remains fixed relative to the distant stars over short time scales, this pole acts as the central pivot point. All visible stars in the North appear to trace circles around this singular, unseen location over the course of the night, with the paths getting smaller the closer a star is to the pole.