No, it is false that Imperialism was the name given to the idea that Americans should expand across the nation to the Pacific Coast, since what you're referring to was known as "Manifest Destiny".
This is false - imperialism wasn't the name given to the idea that Americans should expand across the nation to the Pacific Coast. Imperialism referred to the idea that one nation expands over its borders in the desire of improving its economic standing by exploiting the nation to which it's expanding.
