I tend to see the area around Crimea referred to as "Taurica" when did this start and why did it stop?
Historically, name of a land is typically just a name of people (tribe) who reside there. Like, France is the land of Franks, or Germany is the land of Germans.
So Taurica is the land of "Ταύροι" - some tribe known to ancient Greeks under this name (notably they were mentioned by Herodotus in his "Histories"). But they probably occupied only a (western) part of the peninsula, so there is yet another name - "Cimmeria", though the latter probably applies to both eastern Crimea and to the Taman peninsula. You see, those names belonged to "a political map", rather than to "a geographic one".
But as time goes, the "ancient classical" name of Taurica seem to persist (unlike the tribe), along with later name of "Gothia" (due to Goths, of course).
In 1200s after Mongol invasion Crimean peninsula was divided between several states/tribes: Byzantine Empire, Genoese colonies, Goths, Cumans, Tatar-Mongols.
The word "Crimea" (or Qirim) in Tatar means "a moat". It gradually became the name of the peninsula in XV century after local Tatars (and, most likely, assimilated Cumans) declared independence from the Golden Horde, established own Khanate, and finally conquered the whole peninsula.
In XVIII century Russia conquered Crimean Khanate and made it a part of Russian Empire. Then many Tatar names were forcefully changed into their "classical" Greek counterparts, including "Taurica" itself (see Taurida Governorate). Yet "Crimea" persists as (the only) geographical name of peninsula. Also in 1920s "Crimea" appeared on administrative maps too as part of Soviet Union.