1507, "the western hemisphere, North and South America," in Cartographer Martin Waldseemüller's treatise "Cosmographiae Introductio," from Modern Latin Americanus, after Amerigo Vespucci (1454-1512) who made two trips to the New World as a navigator and claimed to have discovered it. His published works put forward the idea that it was a new continent, and he was first to call it Novus Mundus "New World." Amerigo is more easily Latinized than Vespucci (Latin Vesputius, which might have yielded place-name Vesputia). The sense in English naturally was restricted toward the British colonies, then the United States.
The man's name Amerigo is Germanic, said to derive from Gothic Amalrich, literally "work-ruler." The Old English form of the name has come down as surnames Emmerich, Emery, etc. The Italian fem. form merged into Amelia.
Colloquial pronunciation "Ameri-kay," not uncommon 19c., goes back to at least 1643 and a poem that rhymed the word with away. Amerika "U.S. society viewed as racist, fascist, oppressive, etc." is attested from 1969; the spelling is German but may also suggest the KKK.
It is a thousand pities that the puny witticisms of a few professional objectors should have the power to prevent, even for a year, the adoption of a name for our country. At present we have, clearly, none. There should be no hesitation about "Appalachia." In the first place, it is distinctive. "America" is not, and can never be made so. We may legislate as much as we please, and assume for our country whatever name we think right — but to use it will be no name, to any purpose for which a name is needed, unless we can take it away from the regions which employ it at present. South America is "America," and will insist upon remaining so. [Edgar Allan Poe, 1846]
FREDONIA, FREDONIAN, FREDE, FREDISH, &c. &c. These extraordinary words, which have been deservedly ridiculed here as well as in England, were proposed sometime ago, and countenanced by two or three individuals, as names for the territory and people of the United States. The general term American is now commonly understood (at least in all places where the English language is spoken,) to mean an inhabitant of the United States; and is so employed, except where unusual precision of language is required. [Pickering, 1816]