SiberiaKhanate is an anachronistic rendering of its actual name Khanate of Sibir, a Tatar khanate in the later Russian Siberia.
During the 1450's, Muhammad Shaybani (A descendant of Shayban but not a Khan of Sibir) was forced southwards from Siberia and founded the Uzbek Khanate on the remains of the Timurid Empire.
In a sense, the khanate lived on in the subsidiary title "Tsar of Siberia" which became part of the full imperial style of the Russian Autocrats.