Did the Aztecs have a name for the north American continent?

Thanks for your kind words, and for such an interesting question. Our answer is very speculative, as it’s very hard to find authoritative scholarly research on this subject. The best source we’ve come across so far is Gordon Brotherston’s Book of the Fourth World (1992). In it the author references the post-invasion Lienzo de Tlaxcala, which records the campaigns of conquest waged through Mesoamerica from 1519 onwards: ‘At its extremes the Tlaxcala Lienzo shows us the setting sun of Tonatiuh Ihuecotzian, the Californian Far West [pic 1 L]; and to the north, the image of Cibola and its seven city gates, usually identified with the Zuni, with which the text ends’ (pic 1 R).
This in itself, of course, only shows that these distant lands were known early on in New Spain, the result of treasure-seeking expeditions launched by successive colonial regimes.

Pic 1: Tonatiuh Ihuecotian (California), Lienzo de Tlaxcala fol. 73 (detail) (L); gates at Cibola, or Zuni (drawing based on) Tlaxcala Codex scene 156 (R)

The logical conclusion would seem to be that yes, the peoples of Central Mexico WERE aware of the existence of cultured societies way to the north of their homeland, but we don’t have any record of what name, if any, they gave to these distant lands. The Mexica called their homeland Anáhuac (‘Near the Water’), initially referring to their territory in the Basin of Mexico but with the expansion of the ‘Aztec empire’ it became a term applicable to the known world in total, stretching from the Pacific to the Atlantic coasts.

Pic 3: Which design is from central Mexico, which is from Illinois? (Clues below...!)