Funnily, all uses of "America" for the whole continent (including the north) are misinterpretations of the original map drawn by Mr Waldseemüller, who invented the name "America" in the first and used it for Brazil.

On the same map some designation for the northern part of the continent can also be found, stating that it was a province discovered by the command of the king of Castille:

https://upload.wikimedia.org/wikipedia/commons/c/c0/Waldseemuller_map_2.jpg

So, the only logical step will be to name North-America as "New Castille" from now on, to correct for the screw-up of the post-Waldseemüller map-reading-noobs.