What is the term for the 26,000-year cycle completed by the pole star's change?

Precession - the slow wobble of Earth's axis, like a spinning top leaning over, tracing a circle on the sky about every 26,000 years. Polaris is only temporarily the pole star; Thuban held the job when the pyramids were built, and Vega will have it in about 12,000 years.

Hipparchus noticed it around 130 BC by comparing his own star positions with Babylonian records 150 years older and finding everything shifted. Detecting a drift of one degree per 72 years from other people's data, without a telescope, is one of the more impressive measurements in ancient science, and it required trusting that the earlier records were accurate enough to differ from.

It quietly broke astrology. The signs were fixed to the constellations over two thousand years ago and the sky has since slid by about a whole sign, so the tropical zodiac in general use no longer matches where the Sun actually is - someone called a Leo is usually standing under Cancer. Precession also shifts which hemisphere leans towards the Sun at closest approach, which is part of why ice ages come and go on cycles of tens of thousands of years.