I know that the "United States of America" is the only country with the word "America" in its name. I know that the "United Mexican States" also has the words "united" and states" in its name -- are Mexicans "USians" too?
I know that most Mexicans, by default, refer to people from the United States as "Americanos." I know that most Canadians are quite happy not to be confused with the "Americans" from south of their border.
I know that people from the United States of America have been referred to as "Americans" for over 200 years. I know that when someone makes it a point to start calling someone else by a different name than the one that's preferred, that person is usually pushing some outside agenda and should not be taken seriously in the conversation at-hand.
TL;DR: What does any of this have to do with your point about Israel and Gaza?