臺灣

Appears to be first attested in a memorial to the imperial government by official He Kai (何楷) in 1635:

:

Officially, no later than 1684 with the creation of Taiwan Prefecture (臺灣府). A phonetic transliteration of an ethnonym of a tribe in the southwest part of the island in the area of Anping, Tainan, southwest Taiwan, variously recorded in Dutch records as Tayouan or Tayowan or Taiouwang. A Dutch missionary referred to this group as Taiouwang no later than 1636. Other phonetic transliterations in Chinese characters included 大員 [1603], 大圓 [1617], 臺員, and 大灣 [circa 1624], as placenames initially referring to a sandbank peninsula that later silted up now wholly part of the island in the area of modern-day Anping District, Tainan that eventually became the name of the entire island.

Possibly derived from Siraya.

By surface analysis, 臺 /台 (tái, “terraced”) + 灣 /湾 (wān, “bay”).