Early American Donkey Kong arcade machines used US Set 1 and the game title had "1981 Nintendo" as the copyright. Later US boards used Set 2 and Nintendo changed the copyright title to "1981 Nintendo of America". What was the main reason for changing the wording of the copyright title?
Quite simple, Nintendo of America was incorporated in 1982 in Redmond (!). Nintendo of America acted from there on as sole copyright holder for all sales within the US.
Before that US sales where in the name of the Nintendo (Japan). But copyrights are still today a national issue, where foreign companies may have a hard time to get their rights acknowledged. Even more so in the 80s.