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1507, 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.

The 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." first attested 1969; the spelling is German, but may also suggest the KKK.
It is interesting to remember that the song which is essentially Southern -- "Dixie" -- and that which is essentially Northern -- "Yankee Doodle" -- never really had any serious words to them. ["The Bookman," June 1910]

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]