Why was the Platonic year named after Plato?
The Platonic Year was named after Plato because of his conviction of the intimate relationship between space and time. Plato believed that the heavens were "designed" by God for the measurement of time. In his view of the solar system, Plato placed the Moon, the Sun and the planets in "whorls" around the Earth which orbited at different rates. He called one complete cycle of the bodies in this configuration a Perfect Year. Estimates of a Perfect Year's length are a few hundred thousand years.
Though some of Plato's ideas concerning the solar system are now known to be incorrect, the Earth does complete one long cycle on timescales comparable to the (non-existent) Perfect Year. Because of the precession of the Earth's spin, the direction along which the Earth's axis of rotation is aligned drifts among the stars, completing one round in about thirty thousand years. This cycle has been named the Platonic year in honor of Plato's revolutionary ideas.
For more information about Plato's astronomy and the Platonic year, check out this link.
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