"Yankee" is derogatory or at best playful. "Usonians" isn't a word or in the form of a word.

"American" or "America" in this context is short for "United States of America" and has been used that way for generations, here and around the world. For the geographical term, use "North America," etc.; for the cultural, perhaps use "Anglo-America" or "Latin America."

Actually quite interesting that there is no good naming for people from the USA. Its just the patriotic BS that has spewed over there for decades that has lead to USA people believing they are the only Americans :)